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solv-int/9512005 | Rinat Kashaev | R.M. Kashaev | On Discrete 3-Dimensional Equations Associated with the Local
Yang-Baxter Relation | 10 pages, LaTeX, no figures | null | 10.1007/BF01815521 | ENSLAPP-L-569/95 | solv-int nlin.SI | null | The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a
proper generalization to 3 dimensions of the zero curvature relation. Recently,
Korepanov has constructed an infinite set of integrable 3-dimensional lattice
models, and has related them to solutions to the local YBE. The simplest
Korepanov's model is related to the star-triangle relation in the Ising model.
In this paper the corresponding discrete equation is derived. In the continuous
limit it leads to a differential 3d equation, which is symmetric with respect
to all permutations of the three coordinates. A similar analysis of the
star-triangle transformation in electric networks leads to the discrete
bilinear equation of Miwa, associated with the BKP hierarchy. Some related
operator solutions to the tetrahedron equation are also constructed.
| 2009-10-28 |
solv-int/9512006 | Costas Efthimiou | S. A. Apikyan and C. J. Efthimiou | Integrable Models of the CFT on Hyper-Elliptic Surfaces | Postscript file available at
http://www.tau.ac.il/~costas/papers/HES-2.ps; revised version to appear in
Phys. Lett. B | Phys.Lett. B383 (1996) 397-402 | 10.1016/0370-2693(96)00666-1 | Tel Aviv University Preprint TAUP 2308-95 | solv-int hep-th nlin.SI | null | In this letter, we continue the work we started at a previous paper and we
propose new series of integrable models in quantum field theory. These models
are obtained as perturbed models of the minimal conformal field theories on the
hyper-elliptic surfaces by particular relevant operators of the untwisted
sector. The quantum group symmetry of the models is also discussed.
| 2009-10-28 |
solv-int/9512007 | Juri Suris | Yu.B.Suris (University of Bremen, Germany) | Discrete time Bogoyavlensky lattices | 22 pages, LaTeX, revised version (the third lattice discretized now!) | J. Math. Phys., 1996, V. 37, p. 3982-3996. | 10.1063/1.531611 | null | solv-int nlin.SI | null | Discretizations of the Bogoyavlensky lattices are introduced, belonging to
the same hierarchies as the continuous--time systems. The construction
exemplifies the general scheme for integrable discretization of systems on Lie
algebras with $r$--matrix Poisson brackets. An initial value problem for the
difference equations is solved in terms of a factorization problem in a group.
Interpolating Hamiltonian flow is found.
| 2009-10-28 |
solv-int/9512008 | Henrik Aratyn | H. Aratyn, E. Nissimov and S. Pacheva | Constrained KP Hierarchies: Darboux-B\"acklund Solutions and Additional
Symmetries | LaTeX, 15 pgs, To be published in Proceedings of the second Summer
Workshop, Razlog/Bulgaria, Aug-Sept 1995 | null | null | INRNE-TH/95-15, UICHEP-TH/95-14 | solv-int hep-th nlin.SI | null | We illustrate the basic notions of {\em additional non-isospectral
symmetries} and their interplay with the discrete {\em \DB transformations} of
integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili}
(\cKP) integrable hierarchies. As a main application we present the solution of
discrete multi-matrix string models in terms of Wronskian $\t$-functions of
graded $SL(m,1)$ \cKP hierarchies.
| 2008-02-03 |
solv-int/9601001 | Jose Carlos Brunelli P. | J. C. Brunelli | Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy | 16 pages, plain TeX | Rev.Math.Phys. 8 (1996) 1041-1054 | 10.1142/S0129055X96000378 | null | solv-int hep-th nlin.SI | null | We study from a Hamiltonian point of view the generalized dispersionless KdV
hierarchy of equations. From the so called dispersionless Lax representation of
these equations we obtain three compatible Hamiltonian structures. The second
and third Hamiltonian structures are calculated directly from the r-matrix
approach. Since the third structure is not related recursively with the first
two ones the generalized dispersionless KdV hierarchy can be characterized as a
truly tri-Hamiltonian system.
| 2009-10-30 |
solv-int/9601002 | Manuel Manas | F. Guil, M. Ma\~nas | The Three-Wave Resonant Interaction: Deformation of the Plane-Wave
Solutions and Darboux Transformations | 16 pages, AMSLaTeX | null | null | null | solv-int nlin.SI | null | The plane wave solutions of the three-wave resonant interaction in the plane
are considered. It is shown that rank-one constraints over the right
derivatives of invertible operators on an arbitrary linear space gives
solutions of the three-wave resonant interaction that can be understood as a
Darboux transformation of the plane wave solutions. The method is extended
further to obtain general Darboux transformations: for any solution of the
three-wave interaction problem and vector solutions of the corresponding Lax
pair large families of new solutions, expressed in terms of Grammian type
determinants of these vector solutions, are given.
| 2008-02-03 |
solv-int/9601003 | Wen-Xiu Ma | Wen-Xiu Ma and Benno Fuchssteiner (University of Paderborn) | The Bi-Hamiltonian Structure of the Perturbation Equations of KdV
Hierarchy | 9 pages, Latex, submitted to Phys. Lett. A | null | 10.1016/0375-9601(96)00112-0 | null | solv-int nlin.SI | null | The bi-Hamiltonian structure is established for the perturbation equations of
KdV hierarchy and thus the perturbation equations themselves provide also
examples among typical soliton equations. Besides, a more general
bi-Hamiltonian integrable hierarchy is proposed and a remark is given for a
generalization of the resulting perturbation equations to $1+2$ dimensions.
| 2015-06-26 |
solv-int/9601004 | Michio Jimbo | M. Jimbo, H. Sakai, A. Ramani and B. Grammaticos | Bilinear structure and Schlesinger transforms of the $q$-P$_{\rm III}$
and $q$-P$_{\rm VI}$ equations | 10 pages, Plain TeX | null | 10.1016/0375-9601(96)00336-2 | null | solv-int nlin.SI | null | We show that the recently derived ($q$-) discrete form of the Painlev\'e VI
equation can be related to the discrete P$_{\rm III}$, in particular if one
uses the full freedom in the implementation of the singularity confinement
criterion. This observation is used here in order to derive the bilinear forms
and the Schlesinger transformations of both $q$-P$_{\rm III}$ and $q$-P$_{\rm
VI}$.
| 2009-10-30 |
solv-int/9601005 | Leon Jerome | M. Boiti, J. Leon, F. Pempinelli, (Physique Mathematique et Theorique,
CNRS, F-34095 MONTPELLIER) | Nonlinear Discrete Systems with Nonanalytic Dispersion Relations | RevTex file, to appear in Journ. Math. Phys | null | 10.1063/1.531542 | null | solv-int nlin.SI | null | A discrete system of coupled waves (with nonanalytic dispersion relation) is
derived in the context of the spectral transform theory for the Ablowitz Ladik
spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave
evolution problem is a discrete version of the stimulated Raman scattering
equations, and it is shown to be solvable for arbitrary boundary value of the
two radiation fields and initial value of the medium state. The spectral
transform is constructed on the basis of the D-bar approach.
| 2009-10-30 |
solv-int/9601006 | Ron Perline | Ron Perline (Drexel University) | Localized Induction Hierarchy and Weingarten Systems | AMSTeX file (10 pages) with one Postscript graphic; submitted to
Physics Letters A | null | 10.1016/0375-9601(96)00513-0 | null | solv-int nlin.SI | null | We describe a method of constructing Weingarten systems of triply orthogonal
coordinates, related to the localized induction equation hierarchy of
integrable geometric evolution equations
| 2009-10-30 |
solv-int/9602001 | Harold Widom | Harold Widom (University of California, Santa Cruz) | Some Classes of Solutions to the Toda Lattice Hierarchy | LaTeX file, 18 pages. Results generalized and applications to the
Toda equations added | Commun.Math.Phys. 184 (1997) 653-667 | 10.1007/s002200050078 | null | solv-int hep-th math.FA nlin.SI | null | We apply an analogue of the Zakharov-Shabat dressing method to obtain
infinite matrix solutions to the Toda lattice hierarchy. Using an operator
transformation we convert some of these into solutions in terms of integral
operators and Fredholm determinants. Others are converted into a class of
operator solutions to the $l$-periodic Toda hierarchy.
| 2009-10-30 |
solv-int/9602002 | J. C. de Gier | Jan de Gier, Bernard Nienhuis (University of Amsterdam) | Exact Solution of an Octagonal Random Tiling Model | 4 pages,3 Postscript figures, uses revtex | Phys. Rev. Lett. 76 (1996) 2918-2921 | 10.1103/PhysRevLett.76.2918 | ITFA 95-24 | solv-int cond-mat hep-th nlin.SI | null | We consider the two-dimensional random tiling model introduced by Cockayne,
i.e. the ensemble of all possible coverings of the plane without gaps or
overlaps with squares and various hexagons. At the appropriate relative
densities the correlations have eight-fold rotational symmetry. We reformulate
the model in terms of a random tiling ensemble with identical rectangles and
isosceles triangles. The partition function of this model can be calculated by
diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations
can be solved providing {\em exact} values of the entropy and elastic
constants.
| 2011-11-29 |
solv-int/9603001 | John Harnad | M.R. Adams, J. Harnad, and J. Hurtubise | Darboux Coordinates on Coadjoint Orbits of Lie Algebras | AMSTeX 16pgs | Lett.Math.Phys. 40 (1997) 41-57 | null | CRM 2338 (1996) | solv-int hep-th nlin.SI | null | The method of constructing spectral Darboux coordinates on finite dimensional
coadjoint orbits in duals of loop algebras is applied to the one pole case,
where the orbit is identified with a coadjoint orbit in the dual of a finite
dimensional Lie algebra. The constructions are carried out explicitly when the
Lie algebra is $\frak{sl}(2,\bold R),\ \frak{sl}(3, \bold R),$ and
$\frak{so}(3, \bold R)$, and for rank two orbits in $\frak{so}(n, \bold R)$. A
new feature that appears is the possibility of identifying spectral Darboux
coordinates associated to ``dynamical" choices of sections of the associated
eigenvector line bundles; i.e. sections that depend on the point within the
given orbit.
| 2008-02-03 |
solv-int/9603002 | Basile Grammaticos | Y. Ohta, A. Ramani, B. Grammaticos and K.M. Tamizhmani | From Discrete to Continuous Painlev\'e Equations: A Bilinear Approach | 9 pages, plainTeX | null | 10.1016/0375-9601(96)00292-7 | null | solv-int nlin.SI | null | We present the bilinear forms of the (continuous) Painlev\'e equations
obtained from the continuous limit of the analogous expresssions for the
discrete ones. The advantage of this method is that it leads to very
symmetrical results. A new and interesting result is the bilinearization of the
P$_{\rm VI}$ equation, something that was missing till now.
| 2009-10-30 |
solv-int/9603003 | Basile Grammaticos | B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi and K.M. Tamizhmani | Cellular Automata and Ultra-Discrete Painlev\'e Equations | 8 pages, plainTeX, 2 figures | null | 10.1016/S0375-9601(96)00934-6 | null | solv-int nlin.SI | null | Starting from integrable cellular automata we present a novel form of
Painlev\'e equations. These equations are discrete in both the independent
variable and the dependent one. We show that they capture the essence of the
behavior of the Painlev\'e equations organizing themselves into a coalescence
cascade and possessing special solutions. A necessary condition for the
integrability of cellular automata is also presented.
| 2009-10-30 |
solv-int/9603004 | V. Z. Enolskii | Victor Enolskii (Institute of Magnetism, Kiev ) and Mario Salerno
(University of Salerno ) | Lax representation for two--particle dynamics splitting on two tori | 9 pages, LaTeX | null | 10.1088/0305-4470/29/17/002 | null | solv-int nlin.SI | null | Lax representation in terms of $2\times 2$ matrices is constructed for a
separable multiply--periodic system splitting on two tori. Hyperelliptic
Kleinian functions and their reduction to elliptic functions are used.
| 2009-10-30 |
solv-int/9603005 | V. Z. Enolskii | Victor Buchstaber (Research Institute of Physico-Technical and
Radio-Technical Measurements, VNIIFTRI, Mendeleevo), Victor Enolskii and
Dmitri Leykin (NASU Institute of Magnetism, Kiev ) | Hyperelliptic Kleinian functions and applications | 24 pages, AMSLaTeX2e | null | null | null | solv-int nlin.SI | null | We develop the theory of hyperelliptic Kleinian functions. As applications we
consider construction of the explicit matrix realization of the hyperelliptic
Kummer varieties, differential operators to have the hyperelliptic curve as
spectral variety, solution of the KdV equations by Kleinian functions.
| 2008-02-03 |
solv-int/9603006 | V. Kuznetsov | F.W. Nijhoff, V.B. Kuznetsov, E.K. Sklyanin and O. Ragnisco | Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system | 14 pages, LaTex, equations.sty, no figures, comment on explicit
non-relativistic limit is added | J.Phys. A29 (1996) L333-L340 | 10.1088/0305-4470/29/13/005 | University of Leeds, March 1996 | solv-int hep-th math.QA nlin.SI q-alg | null | The classical r-matrix structure for the generic elliptic
Ruijsenaars-Schneider model is presented. It makes the integrability of this
model as well as of its discrete-time version that was constructed in a recent
paper manifest.
| 2009-10-30 |
solv-int/9603007 | null | Mario Salerno (Department of Theoretical Physics, University of
Salerno, Salerno, Italy) | The Hubbard model on a complete graph: Exact Analytical results | Email:SALERNO@csied.unisa.it | Z. Phys. B 99 (1996) 469 | 10.1007/s002570050064 | null | solv-int cond-mat nlin.SI | null | We derive the analytical expression of the ground state of the Hubbard model
with unconstrained hopping at half filling and for arbitrary lattice sites.
| 2009-10-30 |
solv-int/9603008 | null | Mario Salerno (Department of Theoretical Physics, University of
Salerno) | Ferromagnetic ground states of the Hubbard model on a complete graph | latex file | Z. Phys. B 101 (1996) 619 | 10.1007/s002570050254 | null | solv-int cond-mat nlin.SI | null | We use group theory to derive the exact analytical expression of the
ferromagnetic ground states of the Hubbard model on a complete graph for
arbitrary lattice sites f and for arbitrary fillings $N$. We find that for
$t>0$ and for $N=f+1$ the ground state is maximally ferromagnetic with total
spin $S=(f-1)/2$. For $N > f+1$ the ground state is still ferromagnetic but
becomes degenerate with respect to $S$.
| 2009-10-30 |
solv-int/9603009 | null | Mario Salerno (Department of Theoretical Physics, University of
Salerno, Salerno, Italy) | SO(4) invariant basis functions for strongly correlated Fermi systems | salerno@csied.unisa.it | Phys. Lett. A 217(1996)269 | 10.1016/0375-9601(96)00338-6 | null | solv-int cond-mat nlin.SI | null | We show how to construct SO(4) invariant functions for strongly correlated
Fermi systems on lattices of finite sizes. We illustrate the method on the case
of the 1D Hubbard chain with four and with six sites.
| 2009-10-30 |
solv-int/9603010 | Benzion Shklyar | B. Shklyar (Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel) | Approximate Controlability by Control Constraints for Infinite
Dimensional Systems | 12 pages, LaTeX | null | null | bimacs-96 | solv-int nlin.SI | null | For linear infinite systems the approximate controllability problem by
control constraints is considered. Controllability conditions represented via
system parameters are obtained. Partial differential control systems and
control systems with delays are considered as an example.
| 2008-02-03 |
solv-int/9603011 | null | Yuri B. Suris (University of Bremen) | Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are
governed by the same r-matrix | null | Phys. Lett. A225, 1997, p. 253-262. | 10.1016/S0375-9601(96)00897-3 | null | solv-int nlin.SI | null | We demonstrate that in a certain gauge the elliptic Ruijsenaars--Schneider
models admit Lax representation governed by the same dynamical $r$--matrix as
their non--relativistic counterparts (Calogero--Moser models). This phenomenon
was previously observed for the rational and hyperbolic models.
| 2015-06-26 |
solv-int/9603012 | Ken Umeno | Ken Umeno (Brain Information Processing Group of RIKEN) | Non-perturbative non-integrability of non-homogeneous nonlinear lattices
induced by non-resonance hypothesis | Latex, 21 pages, to appear in Physica D (1996), ps.Z file available
at http://www.bip.riken.go.jp/irl/chaosken/reulam.ps.Z | Physica D94(1996)116-134. | 10.1016/0167-2789(96)88314-X | null | solv-int nlin.SI | null | We prove the non-integrability (non-existence of additional analytic
conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU)
lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method
about the variational equations. The key to this analysis is that the normal
variational equations along a certain solution happen to be in a type of Lam\'e
equations. We also introduce the classification problem towards non-homogeneous
nonlinear lattices including FPU lattices using non-integrability preserving
transformation.
| 2015-06-26 |
solv-int/9604001 | Hsien-chung Kao | Hsien-chung Kao, Shih-Chang Lee, and Wen-Jer Tzeng | Farey Tree and the Frenkel-Kontorova Model | 9 pages, uses Revtex. | null | 10.1103/PhysRevE.55.2628 | null | solv-int cond-mat nlin.SI | null | We solved the Frenkel-Kontorova model with the potential $V(u)= -\frac{1}{2}
|\lambda|(u-{\rm Int}[u]-\frac{1}{2})^2$ exactly. For given $|\lambda|$, there
exists a positive integer $q_c$ such that for almost all values of the tensile
force $\sigma$, the winding number $\omega$ of the ground state configuration
is a rational number in the $q_c$-th level Farey tree. For fixed $\omega=p/q$,
there is a critical $\lambda_c$ when a first order phase transition occurs.
This phase transition can be understood as the dissociation of a large molecule
into two smaller ones in a manner dictated by the Farey tree. A kind of
``commensurate-incommensurate'' transition occurs at critical values of
$\sigma$ when two sizes of molecules co-exist. ``Soliton'' in the usual sense
does not exist but induces a transformation of one size of molecules into the
other.
| 2009-10-30 |
solv-int/9604002 | A. M. Carroll | Daniel Stubbs (University of Western Ontario) | Analytic Structure of the Landau-Ginzburg Equation in 2+1 Dimensions | 6 pages, LaTeX, submitted to the Journal of Mathematical Physics | null | null | null | solv-int nlin.SI | null | In this paper, two methods are employed to investigate for which values of
the parameters, if any, the two-dimensional real Landau-Ginzburg equation
possesses the Painleve property. For an ordinary differential equation to have
the Painleve property all of its solutions must be meromorphic but for partial
differential equations there are two inequivalent definitions, one a direct
investigation of a Laurent series expansion and the other indirect and relying
on a knowledge of the continuous symmetry group of the equation. We check both
methods for the Landau-Ginzburg equation in 2+1 dimensions and each one yields
that this equation does not possess the Painleve property for any values of the
parameters.
| 2008-02-03 |
solv-int/9604003 | null | E. Alfinito, M. Leo, R. A. Leo, M. Palese and G. Soliani | Algebraic properties of the 1+1 dimensional Heisenberg spin field model | Tex file, 10 pages | Lett. Math. Phys., {\bf 32}, 241 (1994) | 10.1007/BF00750666 | null | solv-int nlin.SI | null | The Estabrook-Wahlquist prolongation method is applied to the (compact and
noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a
special realization (an algebra of the Kac-Moody type) of the arising
incomplete prolongation Lie algebra, a whole family of nonlinear field
equations containing the original Heisenberg system is generated.
| 2009-10-30 |
solv-int/9604004 | Wen-Xiu Ma | W. X. Ma and B. Fuchssteiner | Integrable Theory of the Perturbation Equations | 27 pages, latex, to appear in Chaos, Soliton & Fractals | null | 10.1016/0960-0779(95)00104-2 | null | solv-int hep-th nlin.SI | null | An integrable theory is developed for the perturbation equations engendered
from small disturbances of solutions. It includes various integrable properties
of the perturbation equations: hereditary recursion operators, master
symmetries, linear representations (Lax and zero curvature representations) and
Hamiltonian structures etc. and provides us a method to generate hereditary
operators, Hamiltonian operators and symplectic operators starting from the
known ones. The resulting perturbation equations give rise to a sort of
integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP
equation) are carefully carried out.
| 2015-06-26 |
solv-int/9604005 | Holger Frahm | Fabian H. L. Essler, Holger Frahm, Alexander R. Its and Vladimir E.
Korepin | Painlev\'e Transcendent Describes Quantum Correlation Function of the
XXZ Antiferromagnet away from the free-fermion point | 10 pages, LaTeX2e | J.Phys.A29:5619-5626,1996 | 10.1088/0305-4470/29/17/032 | OUTP-96-16S, ITP-UH-06/96 | solv-int cond-mat hep-th nlin.SI | null | We consider quantum correlation functions of the antiferromagnetic
spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that
for a magnetic field close to the critical field $h_c$ (for the critical
magnetic field the ground state is ferromagnetic) certain correlation functions
can be expressed in terms of the solution of the Painlev\'e V transcendent.
This establishes a relation between solutions of Painlev\'e differential
equations and quantum correlation functions in models of {\sl interacting}
fermions. Painlev\'e transcendents were known to describe correlation functions
in models with free fermionic spectra.
| 2008-11-26 |
solv-int/9605001 | Juri Suris | O.Ragnisco (Rome), Yu.B.Suris (Bremen) | Integrable discretizations of the spin Ruijsenaars-Schneider models | LaTeX file | J.Math.Phys. 38 (1997) 4680-4691 | 10.1063/1.532114 | null | solv-int hep-th nlin.SI | null | Integrable discretizations are introduced for the rational and hyperbolic
spin Ruijsenaars--Schneider models. These discrete dynamical systems are
demonstrated to belong to the same integrable hierarchies as their
continuous--time counterparts. Explicit solutions are obtained for arbitrary
flows of the hierarchies, including the discrete time ones.
| 2009-10-30 |
solv-int/9605002 | Wen-Xiu Ma | Wen-Xiu Ma | Darboux Transformations for a Lax Integrable System in $2n$-Dimensions | Latex, 14 pages, to be published in Lett. Math. Phys | null | 10.1007/s11005-997-3049-3 | null | solv-int nlin.SI | null | A $2n$-dimensional Lax integrable system is proposed by a set of specific
spectral problems. It contains Takasaki equations, the self-dual Yang-Mills
equations and its integrable hierarchy as examples. An explicit formulation of
Darboux transformations is established for this Lax integrable system. The
Vandermonde and generalized Cauchy determinant formulas lead to a description
for deriving explicit solutions and thus some rational and analytic solutions
are obtained.
| 2009-10-30 |
solv-int/9605003 | Yu Song-Ju | Yu.Song-Ju, T.Fukuyama | The Painlev\'e Test of Higher Dimensional KdV Equation | 7 pages, LaTeX | null | null | null | solv-int nlin.SI | null | We argue the integrability of the generalized KdV(GKdV) equation using the
Painlev\'e test. For $d( \le 2)$ dimensional space, GKdV equation passes the
Painlev\'e test but does not for $d \geq 3$ dimensional space. We also apply
the Ablowitz-Ramani-Segur's conjecture to the GKdV equation in order to
complement the Painlev\'e test.
| 2008-02-03 |
solv-int/9605004 | Ayse Bilge | Ayse Humeyra Bilge | Classification of Integrable Evolution Equations of the Form
$u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$ | 10 pages, no figures | null | null | null | solv-int nlin.SI | null | We obtain the classification of integrable equations of the form
$u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$ using the formal symmetry method of Mikhailov
et al [A.V.Mikhailov, A.B.Shabat and V.V.Sokolov, in {\it What is
Integrability} edited by V.E. Zakharov (Springer-Verlag, Berlin 1991)]. We show
that all such equations can be transformed to an integrable equation of the
form $v_t=v_{xxx}+f(v,v_x,v_{xx})$ using transformations
$\Phi(x,t,u,v,u_x,v_x)=0$, and the $u_{xx}$ dependence can be eliminated except
for two equations.
| 2008-02-03 |
solv-int/9605005 | Harm Dorren | H.J.S. Dorren and R.K. Snieder | A stability analysis for the Korteweg-de Vries equation | 15 pages LaTeX. The figures are available upon request
(dorren@geof.ruu.nl) | null | null | null | solv-int nlin.SI | null | In this paper the stability of the Korteweg-de Vries (KdV) equation is
investigated. It is shown analytically and numerically that small perturbations
of solutions of the KdV-equation introduce effects of dispersion, hence the
perturbation propagates with a different velocity then the unperturbed
solution. This effect is investigated analytically by formulating a
differential equation for perturbations of solutions of the KdV-equation. This
differential equation is solved generally using an Inverse Scattering Technique
(IST) using the continuous part of the spectrum of the Schr\"{o}dinger
equation. It is shown explicitly that the perturbation consist of two parts.
The first part represents the time-evolution of the perturbation only. The
second part represents the interaction between the perturbation and the
unperturbed solution. It is shown explicitly that singular non-dispersive
solutions of the KdV-equation are unstable.
| 2008-02-03 |
solv-int/9605006 | Juri Suris | Yuri B. Suris (Bremen) | New integrable systems related to the relativistic Toda lattice | LaTeX, 22 pp. Substantially extended version: several new systems
added! | J. Phys. A: Math. and Gen., 1997, V. 30, p. 1745-1761. | 10.1088/0305-4470/30/5/035 | null | solv-int nlin.SI | null | New integrable lattice systems are introduced, their different integrable
discretization are obtained. B\"acklund transformations between these new
systems and the relativistic Toda lattice (in the both continuous and discrete
time formulations) are established.
| 2009-10-30 |
solv-int/9605007 | null | A. A. Andrianov, M. V. Ioffe and D. N. Nishnianidze | Higher Order SUSY in Quantum Mechanics and Integrability of
Two-dimensional Hamiltonians | 11 pages, LaTeX | null | null | SPbU-IP-96-12 | solv-int hep-th nlin.SI | null | The new method based on the SUSY algebra with supercharges of higher order in
derivatives is proposed to search for dynamical symmetry operators in 2-dim
quantum and classical systems. These symmetry operators arise when closing the
SUSY algebra for a wide set of potentials. In some cases they are of 2-nd order
in derivatives. The particular solutions are obtained also for potentials
accepting symmetry operators of 4-th order. The investigation of quasiclassical
limit of the SUSY algebra yields new classical integrals of motion for a
certain type of systems which are polynomials of 4-th order in momenta. The
general SUSY-inspired algorithm to construct classical systems with additional
integrals of motion is outlined.
| 2008-02-03 |
solv-int/9605008 | Adrian-Stefan Carstea | A. S. C\^arstea and D. Grecu | On a class of rational and mixed soliton-rational solutions of Toda
lattice | 10 pages, Latex | null | 10.1143/PTP.96.29 | FT-413-1996, Inst.Atomic Physics, Bucharest, Romania | solv-int nlin.SI | null | A class of rational solutions of Toda lattice satisfying certain Backlund
transformations and a class of mixed rational-soliton solutions (quasisolitons)
in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an
extended class of rational solutions are found using an appropriate recursion
relation. They are also solutions of Boussinesq equation and it is conjectured
that there is a larger class of common solutions of both equations.
| 2009-10-30 |
solv-int/9605009 | Wen-Xiu Ma | Wen-Xiu Ma and Benno Fuchssteiner | Binary Nonlinearization of Lax Pairs | 8 pages, latex, to appear in the Proceedings of Nonlinear Physics,
Italy | null | null | null | solv-int nlin.SI | null | A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax
pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs
are nonlinearized into a hierarchy of commutative finite dimensional integrable
Hamiltonian systems and explicit integrals of motion may also be generated. The
corresponding binary nonlinearization procedure leads to a sort of involutive
solutions to every system in soliton hierarchy which are all of finite gap. An
illustrative example is given in the case of AKNS soliton hierarchy.
| 2008-02-03 |
solv-int/9605010 | Juri Suris | Yuri B. Suris (Bremen) | A new integrable system related to the Toda lattice | LaTeX, 14 pp | J. Phys. A: Math. and Gen., 1997, V. 30, p. 2235-2249. | 10.1088/0305-4470/30/6/041 | null | solv-int nlin.SI | null | A new integrable lattice system is introduced, and its integrable
discretizations are obtained. A B\"acklund transformation between this new
system and the Toda lattice, as well as between their discretizations, is
established.
| 2009-10-30 |
solv-int/9606001 | Dr. Elena I. Ganzha | E. I. Ganzha (Krasnoyarsk State Pedagogical University) | On completeness of the Moutard transformations | 6 pages (17 Kbytes), standard LaTeX 2.09, run twice to get the right
cross-references. Resubmitted with the only correction: acknowledgment of
grant RBFR 96-01-00050 support | null | null | null | solv-int nlin.SI | null | In this paper we solve positively the problem of (local) density of the
"potentials" M(x,y) of the Moutard equation, u_{xy} = M(x,y) u, u=u(x,y), (used
in many papers for construction of exact solutions of (2+1)-dimensional
integrable systems) obtainable from a given initial potential with consecutive
Moutard transformations.
| 2008-02-03 |
solv-int/9606002 | Dr. Elena I. Ganzha | E. I. Ganzha (Krasnoyarsk State Pedagogical University) | On completeness of the Ribaucour transformations for triply orthogonal
curvilinear coordinate systems in R^3 | 7 pages (26 Kbytes), standard LaTeX 2.09, run twice to get the right
cross-references. Resubmitted with the only correction: acknowledgment of
grant RBFR 96-01-00050 support | null | null | null | solv-int nlin.SI | null | In this paper we solve positively the problem of (local) density of solutions
of the (2+1)-dimentional integrable system describing triply orthogonal
curvilinear coordinates in R^3 (a (2+1)-dimensional generalization of the
3-wave system) obtainable from a given initial solution with consecutive
B\"acklund transformations (called Ribaucour transformations in classical
differential geometry) in the space of all solutions of the system in question.
| 2008-02-03 |
solv-int/9606003 | S. P. Tsarev | E. T. Ganzha, S. P. Tsarev (Krasnoyarsk State Pedagogical University) | On superposition of the autoBaecklund transformations for
(2+1)-dimensional integrable systems | 11 pages (90 Kbytes), standard LaTeX 2.09, run twice to get the right
cross-references. Resubmitted with the only correction: acknowledgment of
grant RBFR 96-01-00050 support | null | null | null | solv-int nlin.SI | null | The usual superposition formulas for Baecklund transformations of
(2+1)-dimensional integrable systems include quadratures unlike the well known
case of (1+1)-dimensional inegrable systems where the fourth solution is found
with algebraic operations. In the present paper we show how in the case of
(2+1)-dimensional integrable systems one can find an extended formula of
nonlinear superposition such that the resulting solution will be found uniquely
from the given previous solution with algebraic operations.
| 2008-02-03 |
solv-int/9606004 | Dr. Jeremy Schiff | Jeremy Schiff (Dept of Math and Comp Sci, Bar Ilan University) | Symmetries of KdV and Loop Groups | 36 pages (sorry), LaTeX using a4 documentstyle | null | null | null | solv-int hep-th math.QA nlin.SI q-alg | null | A simple version of the Segal-Wilson map from the SL(2,C) loop group to a
class of solutions of the KdV hierarchy is given, clarifying certain aspects of
this map. It is explained how the known symmetries, including Backlund
transformations, of KdV arise from simple, field independent, actions on the
loop group. A variety of issues in understanding the algebraic structure of
Backlund transformations are thus resolved.
| 2008-02-03 |
solv-int/9606005 | Robert Carroll | R. Carroll (Mathematics Dept., University of Illinois, Urbana, IL) | Some survey remarks on Whitham theory and EM duality | Latex, 12 pages | null | null | null | solv-int hep-th nlin.SI | null | The nature of the BA function and its adjoint for KP-Toda is traced through
the averaging method in generating the Whitham equations, differentials, and
symplectic forms, with connections to EM duality.
| 2008-02-03 |
solv-int/9606006 | Barbara Shipman | Barbara Shipman | On the geometry of certain isospectral sets in the full Kostant-Toda
lattice | 22 pages, LaTeX, 7 figures in PicTeX available on request | null | null | null | solv-int nlin.SI | null | We use momentum mappings on generalized flag manifolds and their momentum
polytopes to study the geometry of the level sets of the 1-chop integrals of
the full Kostant-Toda lattice in certain isospectral submanifolds of the phase
space. We derive expressions for these integrals in terms of Pl\"ucker
coordinates on the flag manifold in the case that all eigenvalues are zero and
compare the geometry of the base locus of their level set varieties with the
corresponding geometry for distinct eigenvalues. Finally, we illustrate and
extend our results in the context of the full sl(3,C) and sl(4,C) Kostant-Toda
lattices.
| 2008-02-03 |
solv-int/9606007 | Leonid Bogdanov | L.V. Bogdanov (IINS, Landau Institute, Moscow) and B.G. Konopelchenko
(Universita' degli Studi di Lecce) | Generalized integrable hierarchies and Combescure symmetry
transformations | 17 pages, LaTeX | null | 10.1088/0305-4470/30/5/022 | null | solv-int nlin.SI | null | Unifying hierarchies of integrable equations are discussed. They are
constructed via generalized Hirota identity. It is shown that the Combescure
transformations, known for a long time for the Darboux system and having a
simple geometrical meaning, are in fact the symmetry transformations of
generalized integrable hierarchies. Generalized equation written in terms of
invariants of Combescure transformations are the usual integrable equations and
their modified partners. The KP-mKP, DS-mDS hierarchies and Darboux system are
considered.
| 2009-10-30 |
solv-int/9606008 | Stephanie F. Singer | M. Quinn and S.F. Singer | Loop algebras, gauge invariants and a new completely integrable system | null | null | null | null | solv-int nlin.SI | null | One fruitful motivating principle of much research on the family of
integrable systems known as ``Toda lattices'' has been the heuristic assumption
that the periodic Toda lattice in an affine Lie algebra is directly analogous
to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper
shows that the analogy is not perfect. A discrepancy arises because the natural
generalization of the structure theory of finite-dimensional simple Lie
algebras is not the structure theory of loop algebras but the structure theory
of affine Kac-Moody algebras. In this paper we use this natural generalization
to construct the natural analog of the nonperiodic Toda lattice. Surprisingly,
the result is not the periodic Toda lattice but a new completely integrable
system on the periodic Toda lattice phase space. This integrable system is
prescribed purely in terms of Lie-theoretic data. The commuting functions are
precisely the gauge-invariant functions one obtains by viewing elements of the
loop algebra as connections on a bundle over $S^1$.
| 2008-02-03 |
solv-int/9606009 | Leonid Dickey | L.A.Dickey and W.Strampp | On a generalization of the Fay-Sato identity for KP Baker functions and
its application to constrained hierarchies | LaTeX, 11 pages | null | null | null | solv-int nlin.SI | null | Some new formulas for the KP hierarchy are derived from the differential Fay
identity. They proved to be useful for the $k$-constrained hierarchies
providing a series of determinant identities for them. A differential equation
is introduced which is called ``universal" since it plays an important role for
all the $k$-constrained hierarchies. In the cases $k=1,2$ and 3 explicit
formulas are presented, in all the others recurrence relations are given which
enable one to obtain the identities.
| 2008-02-03 |
solv-int/9606010 | null | Paolo Casati (Dip. di Matematica, Univ. di Milano, Italy), Gregorio
Falqui (SISSA, Trieste, Italy), Franco Magri (Dip. di Matematica, Univ. di
Milano, Italy), and Marco Pedroni (Dip. di Matematica, Univ. di Genova,
Italy) | A Note on Fractional KdV Hierarchies | Final version to appear in J. Math. Phys. Some changes in the order
of presentation, with more emphasis on the geometrical picture. One figure
added (using epsf.sty). 30 pages, Latex | null | 10.1063/1.532110 | null | solv-int nlin.SI | null | We introduce a hierarchy of mutually commuting dynamical systems on a finite
number of Laurent series. This hierarchy can be seen as a prolongation of the
KP hierarchy, or a ``reduction'' in which the space coordinate is identified
with an arbitrarily chosen time of a bigger dynamical system. Fractional KdV
hierarchies are gotten by means of further reductions, obtained by constraining
the Laurent series. The case of sl(3)^2 and its bihamiltonian structure are
discussed in detail.
| 2009-10-30 |
solv-int/9607001 | Hsien-chung Kao | Hsien-chung Kao, Shih-Chang Lee, and Wen-Jer Tzeng | Exact Solution of Frenkel-Kontorova Models with a Complete Devil's
Staircase in Higher Dimensions | 14 pages, uses revtex. Four figures included | null | null | null | solv-int nlin.SI | null | We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic
potential, which has $d$ sub-wells in a period. With careful analysis, we show
that the phase diagram of the minimum enthalpy configurations exhibits the
structure of a complete $d$-dimensional devil's staircase. The winding number
of a minimum enthalpy configuration is locked to rational values, while the
fraction of atoms in each sub-well is locked to values which are
sub-commensurable with the winding number.
| 2008-02-03 |
solv-int/9607002 | Kenji Kajiwara | Kenji Kajiwara (Dept. of Elect. Engin., Doshisha Univ.) and Yasuhiro
Ohta (Dept. Appl. Math., Hiroshima Univ.) | Determinant Structure of the Rational Solutions for the Painlev\'e II
Equation | 16 pages LaTeX. To appear in J. Math. Phys.(1996) | null | 10.1063/1.531648 | null | solv-int nlin.SI | null | Two types of determinant representations of the rational solutions for the
Painlev\'e II equation are discussed by using the bilinear formalism. One of
them is a representation by the Devisme polynomials, and another one is a
Hankel determinant representation. They are derived from the determinant
solutions of the KP hierarchy and Toda lattice, respectively.
| 2009-10-30 |
solv-int/9607003 | Wen-Xiu Ma | Wen-Xiu MA (Paderborn Univ.) and Zi-Xiang ZHOU (Fudan Univ.) | Coupled Integrable Systems Associated with a Polynomial Spectral Problem
and their Virasoro Symmetry Algebras | 8 pages, Plain-tex, to appear in Prog. Theor. Phys | null | 10.1143/PTP.96.449 | null | solv-int nlin.SI | null | An isospectral hierarchy of commutative integrable systems associated with a
polynomial spectral problem is proposed. The resulting hierarchy possesses a
recursion structure controlled by a hereditary operator. The nonisospectral
flows generate the time first order dependent symmetries of the isospectral
hierarchy, which constitute Virasoro symmetry algebras together with
commutative symmetries.
| 2009-10-30 |
solv-int/9607004 | Kirill L. Vaninsky | K.L. Vaninsky | A Convexity Theorem in the Scattering Theory for the Dirac Operator | 20 pages, AMS-TEX | Trans. AMS, vol 350, no. 5, pp. 1895--1911. | null | null | solv-int nlin.SI | null | The Dirac operator enters into zero curvature representation for the cubic
nonlinear Schr\"{o}dinger equation. We introduce and study a conformal map from
the upper half-plane of the spectral parameter of the Dirac operator into
itself. The action variables turn out to be limiting boundary values of the
imaginary part of this map. We describe the image of the momentum map
(convexity theorem) in the simplest case of a potential from the Schwartz
class. We apply this description to the invariant manifolds for the nonlinear
Schr\"{o}dinger equation.
| 2008-02-03 |
solv-int/9607005 | Juri Suris | Yuri B. Suris (University of Bremen) | Some further curiosities from the world of integrable lattice systems
and their discretizations | 14 pp., LaTeX | Symmetries and Integrability of Difference Equations, Eds.
P.Clarkson, F.Nijhoff, Cambridge Univ. Press, 1999, p. 79-94. | null | null | solv-int nlin.SI | null | Unexpected relations are found between the Toda lattice, the relativistic
Toda lattice and the Bruschi--Ragnisco lattice, as well as between their
integrable discretizations.
| 2008-02-03 |
solv-int/9607006 | Nalini Joshi | Nalini Joshi | A Local Asymptotic Analysis of the First Discrete Painlev\'e Equation as
the Discrete Independent Variable Approaches Infinity | 21 pages in LaTeX2e, to appear in \textit{Methods and Applications of
Analysis} | null | null | null | solv-int nlin.SI | null | The first discrete Painlev\'e equation (dPI), which appears in a model of
quantum gravity, is an integrable nonlinear nonautonomous difference equation
which yields the well known first Painlev\'e equation (PI) in a continuum
limit. The asymptotic study of its solutions as the discrete time-step
$n\to\infty$ is important both for physical application and for checking the
accuracy of its role as a numerical discretization of PI. Here we show that the
asymptotic analysis carried out by Boutroux (1913) for PI as its independent
variable approaches infinity can also be achieved for dPI as its discrete
independent variable approaches the same limit.
| 2008-02-03 |
solv-int/9607007 | Nalini Joshi | Nalini Joshi and Gopala K. Srinivasan | The Radius of Convergence and the Well-Posedness of the Painlev\'e
Expansions of the Korteweg-deVries equation | 9 pages in AMSTeX, to appear \textit{Nonlinearity} | null | 10.1088/0951-7715/10/1/005 | null | solv-int nlin.SI | null | In this paper we obtain explicit lower bounds for the radius of convergence
of the Painlev\'e expansions of the Korteweg-de-Vries equation around a movable
singularity manifold ${\Cal S}$ in terms of the sup norms of the arbitrary
functions involved. We use this estimate to prove the well-posedness of the
singular Cauchy problem on ${\Cal S}$ in the form of continuous dependence of
the meromorphic solution on the arbitrary data.
| 2009-10-30 |
solv-int/9607008 | Kirill L. Vaninsky | K.L. Vaninsky | Gibbs' States for Moser-Calogero Potentials | 8 pages, LATEX | Intern J. Mod. Phys. B, vol. 11, no. 1-2, pp. 203-211 (1997) | 10.1142/S0217979297000277 | null | solv-int nlin.SI | null | We present two independent approaches for computing the thermodynamics for
classical particles interacting via the Moser--Calogero potential. Combining
the results we propose the form of equation of state or, what is equivalent,
the asymptotics of the Jacobian between volume elements corresponding two
symplectic structures on the phase space.
| 2009-10-30 |
solv-int/9608001 | Adrian-Stefan Carstea | A. S. C\^arstea | On the dynamics of rational solutions for 1-D generalized Volterra
system | 9 pages, Latex | null | 10.1016/S0375-9601(97)00481-7 | FT-419-1996 | solv-int nlin.SI | null | The Hirota bilinear formalism and soliton solutions for a generalized
Volterra system is presented. Also, starting from the soliton solutions, we
obtain a class of nonsingular rational solutions using the "long wave" limit
procedure of Ablowitz and Satsuma, and appropriate "gauge" transformations.
Their properties are also discussed and it is shown that these solutions
interact elastically with no phase shift.
| 2016-09-08 |
solv-int/9608002 | David Fairlie | D.B. Fairlie | Equations with an infinite number of explicit Conservation Laws | 12 pages, latex, no figures | null | null | DTP/94/41 to appear in Proc.Roy.Soc.Edin | solv-int nlin.SI | null | A large class of first order partial nonlinear differential equations in two
independent variables which possess an infinite set of polynomial conservation
laws derived from an explicit generating function is constructed. The conserved
charge densities are all homogeneous polynomials in the unknown functions which
satisfy the differential equations in question.
The simplest member of the class of equations is related to the Born-Infeld
equation in two dimensions. It is observed that some members of this class
possess identical charge densities. This enables the construction of a set of
multivariable equations with an infinite number of conservation laws.
| 2016-09-08 |
solv-int/9608003 | Wen-Xiu Ma | Wen-Xiu Ma, Qing Ding, Wei-Guo Zhang and Bao-Qun Lu | Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy | 15 pages, plain+ams tex, to be published in Il Nuovo Cimento B | null | 10.1007/BF02743224 | null | solv-int nlin.SI | null | Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different
from the original ones. Binary nonlinearization procedure corresponding to the
Bargmann symmetry constraint is carried out for those Lax pairs. The proposed
Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of
commutative, finite dimensional integrable Hamiltonian systems in the Liouville
sense, which also provides us with new examples of finite dimensional
integrable Hamiltonian systems. A sort of involutive solutions to the
Kaup-Newell hierarchy are exhibited through the obtained finite dimensional
integrable systems and the general involutive system engendered by binary
nonlinearization is reduced to a specific involutive system generated by
mono-nonlinearization.
| 2009-10-30 |
solv-int/9608004 | Tim Baker | T. H. Baker (Uni. of Melbourne) and P. J. Forrester (RIMS, Kyoto
University) | The Calogero-Sutherland Model and Generalized Classical Polynomials | LaTeX 2.09, 41 pages, uses subeqnarray.sty | Commun.Math.Phys. 188 (1997) 175-216 | 10.1007/s002200050161 | RIMS-1094 | solv-int hep-th nlin.SI | null | Multivariable generalizations of the classical Hermite, Laguerre and Jacobi
polynomials occur as the polynomial part of the eigenfunctions of certain
Schr\"odinger operators for Calogero-Sutherland-type quantum systems. For the
generalized Hermite and Laguerre polynomials the multidimensional analogues of
many classical results regarding generating functions, differentiation and
integration formulas, recurrence relations and summation theorems are obtained.
We use this and related theory to evaluate the global limit of the ground state
density, obtaining in the Hermite case the Wigner semi-circle law, and to give
an explicit solution for an initial value problem in the Hermite and Laguerre
case.
| 2009-10-30 |
solv-int/9608005 | YuKui. Zhou | Y-K Zhou (ANU) | Fusion Hierarchies with Open Boundaries and Exactly Solvable Models | 8 pages, no figures, talk given in Tianjin, August 1995. To appear in
"Statistical Models, Yang-Baxter Equation and Related Topics", M. L. Ge and
F. Y. Wu eds, World Scientific, Singapore (1996) | null | null | MRR 079-95 | solv-int cond-mat hep-th nlin.SI | null | The formulation of integrable models with open boundary conditions and the
functional relations of fused transfer matrices are discussed. It is shown that
finite-size corrections to the transfer matrices and unitarity relations of
free energies can be obtained from the functional relations. Unitarity
relations of surface free energies presented in previous papers are also
reviewed.
| 2008-02-03 |
solv-int/9608006 | Ctirad Klimcik | P. Severa | On Simplest Hamiltonian Systems | 2 pages, LaTeX | null | null | null | solv-int nlin.SI | null | Simple Hamiltonian systems, such as mathematical pendulum or Euler equations
for rigid body, are solved without computation. It is nothing but a joke but
maybe you will find it nice.
| 2008-02-03 |
solv-int/9608007 | Simon Labrunie | Simon Labrunie and Robert Conte (Service de physique de l'\'etat
condens\'e, CEA Saclay, Gif-sur-Yvette, France) | A geometrical method towards first integrals for dynamical systems | 15 pages, RevTeX with aps and prb styles | null | 10.1063/1.531772 | preprint SPEC s96/017 | solv-int nlin.SI | null | We develop a method, based on Darboux' and Liouville's works, to find first
integrals and/or invariant manifolds for a physically relevant class of
dynamical systems, without making any assumption on these elements' form. We
apply it to three dynamical systems: Lotka--Volterra, Lorenz and Rikitake.
| 2009-10-30 |
solv-int/9608008 | Simon Labrunie | Simon Labrunie and Robert Conte (Service de physique de l'\'etat
condens\'e, CEA Saclay, Gif-sur-Yvette, France) | Discrete version of the Chazy class III equation | 8 pages, LaTeX | null | null | preprint SPEC s96/039 | solv-int nlin.SI | null | We study the discretisation of the Chazy class III equation by two means: a
discrete Painlev\'e test, and the preservation of a two-parameter solution to
the continuous equation. We get that way a best discretisation scheme.
| 2008-02-03 |
solv-int/9608009 | Kakei Saburo | Saburo Kakei | Common Algebraic Structure for the Calogero-Sutherland Models | 7 pages, LaTeX, no figures, some text and references added, minor
misprints corrected | J. Phys. A29 (1996) L619-L624 | 10.1088/0305-4470/29/24/002 | null | solv-int cond-mat hep-th math.QA nlin.SI q-alg | null | We investigate common algebraic structure for the rational and trigonometric
Calogero-Sutherland models by using the exchange-operator formalism. We show
that the set of the Jack polynomials whose arguments are Dunkl-type operators
provides an orthogonal basis for the rational case.
| 2009-10-30 |
solv-int/9608010 | Jarmo Hietarinta | Jarmo Hietarinta | Nambu tensors and commuting vector fields | 9 pages in LaTeX2e | null | null | null | solv-int hep-th nlin.SI | null | Takhtajan has recently studied the consistency conditions for Nambu brackets,
and suggested that they have to be skew-symmetric, and satisfy Leibnitz rule
and the Fundamental Identity (FI, it is a generalization of the Jacobi
identity). If the n'th order Nambu brackets in dimension N is written in terms
of the Nambu tensor \eta, the FI implies two conditions on it, one algebraic
and one differential. The algebraic part of FI implies decomposability of \eta
and in this letter we show that the Nambu bracket can then be written in terms
of the usual totally antisymmetric n-dimensional tensor and n vector fields D.
Our main result is that the differential part of the FI is satisfied iff the
vector fields D commute. Examples are provided by integrable Hamiltonian
systems. It turns out that then the Nambu bracket itself guarantees that the
motions stays on the manifold defined by the constants of motion of the
integrable system, while the n-1 Nambu Hamiltonians determine the (possibly
non-integrable) motion on this manifold.
| 2008-02-03 |
solv-int/9609001 | Yuji Kodama | Yuji Kodama and Jian Ye | Toda lattices with indefinite metric II: Topology of the iso-spectral
manifolds | LaTex 20 pages with 4 figures | null | null | null | solv-int hep-th nlin.SI | null | We consider the iso-spectral real manifolds of tridiagonal Hessenberg
matrices with real eigenvalues. The manifolds are described by the iso-spectral
flows of indefinite Toda lattice equations introduced by the authors [Physica,
91D (1996), 321-339]. These Toda lattices consist of $2^{N-1}$ different
systems with hamiltonians $H = (1/2) \sum_{k=1}^{N} y_k^2 + \sum_{k=1}^{N-1}
s_ks_{k+1} \exp(x_k-x_{k+1})$, where $s_i=\pm 1$. We compactify the manifolds
by adding infinities according to the Toda flows which blow up in finite time
except the case with all $s_is_{i+1}=1$. The resulting manifolds are shown to
be nonorientable for $N>2$, and the symmetric group is the semi-direct product
of $(\ZZ_2)^{N-1}$ and the permutation group $S_N$. These properties identify
themselves with ``small covers'' introduced by Davis and Januszkiewicz [Duke
Mathematical Journal, 62 (1991), 417-451]. As a corollary of our construction,
we give a formula on the total numbers of zeroes for a system of exponential
polynomials generated as Hankel determinant.
| 2016-09-08 |
solv-int/9609002 | Leon Jerome | M. Boiti, J. Leon, F. Pempinelli | Nonlinear Spectral Characterization of Discrete Data | RevTex file, to appear in Physical Review E | null | 10.1103/PhysRevE.54.5739 | null | solv-int nlin.SI | null | The explicit analytical expression of the Nonlinear Fourier Transform (NFT)
of a finite set of data is provided. Then a simple recursion relation for the
NFT is constructed as a function of the spectral parameter. These tools provide
a complete characterization of the nonlinear coherent structures (solitons,
breathers, ...) present in numerical or experimental data representing the
solution, at a given value of time, of a nonlinear evolution equation (e.g. of
the nonlinear Schroedinger family).
| 2009-10-30 |
solv-int/9609003 | Andrey V. Tsiganov | S. Rauch-Wojciechowski and A.V. Tsiganov | Quasi-point separation of variables for the Henon-Heiles system and a
system with quartic potential | 11 pages, Latex | null | 10.1088/0305-4470/29/23/032 | null | solv-int hep-th nlin.SI | null | We examine the problem of integrability of two-dimensional Hamiltonian
systems by means of separation of variables. The systematic approach to
construction of the special non-pure coordinate separation of variables for
certain natural two-dimensional Hamiltonians is presented. The relations with
SUSY quantum mechanics are discussed.
| 2009-10-30 |
solv-int/9609004 | Pac3 | P.A. Clarkson, E.L. Mansfield and T.J. Priestley (University of Kent,
Canterbury, UK) | Symmetries of a class of Nonlinear Third Order Partial Differential
Equations | 22 pages, tex, Mathematical and Computer Modelling (to appear) | null | null | UKC/IMS/95/27 | solv-int nlin.SI | null | In this paper we study symmetry reductions of a class of nonlinear third
order partial differential equations $u_t -\epsilon u_{xxt} +2\kappa u_x= u
u_{xxx} +\alpha u u_x +\beta u_x u_{xx}$ where $\epsilon$, $\kappa$, $\alpha$
and $\beta$ are arbitrary constants. Three special cases of equation (1) have
appeared in the literature, up to some rescalings. In each case the equation
has admitted unusual travelling wave solutions: the Fornberg-Whitham equation,
for the parameters $\epsilon=1$, $\alpha=-1$, $\beta=3$ and $\kappa=\tfr12$,
admits a wave of greatest height, as a peaked limiting form of the travelling
wave solution; the Rosenau-Hyman equation, for the parameters $\epsilon=0$,
$\alpha=1$, $\beta=3$ and $\kappa=0$, admits a ``compacton'' solitary wave
solution; and the Fuchssteiner-Fokas-Camassa-Holm equation, for the parameters
$\epsilon=1$, $\alpha=-3$ and $\beta=2$, has a ``peakon'' solitary wave
solution. A catalogue of symmetry reductions for equation (1) is obtained using
the classical Lie method and the nonclassical method due to Bluman and Cole.
| 2016-09-08 |
solv-int/9609005 | Pac3 | A.P. Bassom (University of Exeter, UK), P.A. Clarkson (University of
Kent, Canterbury, UK), C.K. Law (National Sun Yat-sen University, Taiwan) and
J.B. McLeod (University of Pittsburgh, USA) | Application of Uniform Asymptotics to the Second Painlev{\'e}
Transcendent | 28 pages, amstex, no figures | null | null | UKC/IMS/96/45 | solv-int nlin.SI | null | In this work we propose a new method for investigating connection problems
for the class of nonlinear second-order differential equations known as the
Painlev{\'e} equations. Such problems can be characterized by the question as
to how the asymptotic behaviours of solutions are related as the independent
variable is allowed to pass towards infinity along different directions in the
complex plane. Connection problems have been previously tackled by a variety of
methods. Frequently these are based on the ideas of isomonodromic deformation
and the matching of WKB solutions. However, the implementation of these methods
often tends to be heuristic in nature and so the task of rigorising the process
is complicated. The method we propose here develops uniform approximations to
solutions. This removes the need to match solutions, is rigorous, and can lead
to the solution of connection problems with minimal computational effort. Our
method is reliant on finding uniform approximations of differential equations
of the generic form ${d^2\phi}/{d\eta^2} = - \xi^2F(\eta,\xi)\phi$ as the
complex-valued parameter $\xi \to \infty.$ The details of the treatment rely
heavily on the locations of the zeros of the function $F$ in this limit. If
they are isolated then a uniform approximation to solutions can be derived in
terms of Airy functions of suitable argument. On the other hand, if two of the
zeros of $F$ coalesce as $|\xi| \to \infty$ then an approximation can be
derived in terms of parabolic cylinder functions. In this paper we discuss both
cases, but illustrate our technique in action by applying the parabolic
cylinder case to the ``classical'' connection problem associated with the
second Painlev{\'e} transcendent. Future papers will show how the technique can
be applied with very little change to the other Painlev{\'e} equations, and to
the wider problem of the asymptotic behaviour of the general solution to any of
these equations.
| 2016-09-08 |
solv-int/9609006 | Wen-Xiu Ma | Wen-Xiu Ma and Kam-Shun Li | Virasoro Symmetry Algebra of Dirac Soliton Hierarchy | 8 pages, latex, to appear in Inverse Problems | null | null | null | solv-int nlin.SI | null | A hierarchy of first-degree time-dependent symmetries is proposed for Dirac
soliton hierarchy and their commutator relations with time-dependent symmetries
are exhibited. Meantime, a hereditary structure of Dirac soliton hierarchy is
elucidated and a Lax operator algebra associated with Virasoro symmetry algebra
is given.
| 2008-02-03 |
solv-int/9609007 | Andrey V. Tsiganov | A.V. Tsiganov (St.Petersburg University) | The Kowalewski top: a new Lax representation | 17 pages, Latex | null | 10.1063/1.531850 | ISRN-LiTH-MAT-R-95-27, 1995 | solv-int nlin.SI | null | The 2x2 monodromy matrices for the Kowalewski top on the Lie algebras e(3),
so(4) and so(3,1) are presented. The corresponding quadratic R-matrix structure
is the dynamical deformation of the standard R-matrix algebras. Some tops and
Toda lattices related to the Kowalewski top are discussed.
| 2009-10-30 |
solv-int/9609008 | Francois Delduc | F. Delduc, L. Gallot | N=2 KP and KdV hierarchies in extended superspace | 18 pages, LaTeX file, important reference added | Commun.Math.Phys. 190 (1997) 395-410 | 10.1007/s002200050246 | ENSLAPP-L-617 | solv-int hep-th nlin.SI | null | We give the formulation in extended superspace of an $N=2$ supersymmetric KP
hierarchy using chirality preserving pseudo-differential operators. We obtain
two quadratic hamiltonian structures, which lead to different reductions of the
KP hierarchy. In particular we find two different hierarchies with the $N=2$
classical super-${\cal W}_n$ algebra as a hamiltonian structure. The relation
with the formulation in $N=1$ superspace is carried out.
| 2009-10-30 |
solv-int/9609009 | Leonid Bogdanov | L.V. Bogdanov (IINS, Landau Institute, Moscow) and B.G. Konopelchenko
(Universit\'a degli Studi di Lecce) | Analytic-bilinear approach to integrable hierarchies. I.Generalized KP
hierarchy | 25 pages, LaTeX | null | null | null | solv-int nlin.SI | null | Analytic-bilinear approach for construction and study of integrable
hierarchies, in particular, the KP hierarchy is discussed. It is based on the
generalized Hirota identity. This approach allows to represent generalized
hierarchies of integrable equations in a condensed form of finite functional
equations. Resolution of these functional equations leads to the
$\tau$-function and addition formulae to it. General discrete transformations
of the $\tau$-function are presented in the determinant form. Closed one-form
and other formulae also arise naturally within the approach proposed.
Generalized KP hierarchy written in terms of different invariants of Combescure
symmetry transformations coincides with the usual KP hierarchy and the mKP
hierarchy.
| 2016-09-08 |
solv-int/9609010 | Tim Baker | T. H. Baker and P. J. Forrester (Uni. of Melbourne) | The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry | LaTeX 2.09, 31 pages | null | 10.1016/S0550-3213(97)00112-0 | null | solv-int math.QA nlin.SI q-alg | null | The Schr\"odinger operators with exchange terms for certain
Calogero-Sutherland quantum many body systems have eigenfunctions which factor
into the symmetric ground state and a multivariable polynomial. The polynomial
can be chosen to have a prescribed symmetry (i.e. be symmetric or
antisymmetric) with respect to the interchange of some specified variables. For
four particular Calogero-Sutherland systems we construct an eigenoperator for
these polynomials which separates the eigenvalues and establishes
orthogonality. In two of the cases this involves identifying new operators
which commute with the corresponding Schr\"odinger operators. In each case we
express a particular class of the polynomials with prescribed symmetry in a
factored form involving the corresponding symmetric polynomials.
| 2016-09-08 |
solv-int/9610001 | Juri Suris | Yuri B. Suris (University of Bremen) | Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky
lattices | 35 pages, LaTeX | J. Math. Phys., 1997, V. 38, p. 4179-4201. | 10.1063/1.532090 | null | solv-int nlin.SI | null | A new Lax representation for the Bogoyavlensky lattice is found, its
$r$--matrix interpretation is elaborated. The $r$--matrix structure turns out
to be related to a highly nonlocal quadratic Poisson structure on a direct sum
of associative algebras. The theory of such nonlocal structures is developed,
the Poisson property of the monodromy map is worked out in the most general
situation. Some problems concerning the duality of Lax representations are
raised.
| 2009-10-30 |
solv-int/9610002 | null | Paolo Casati (Dip. di Matematica, Univ. di Milano, Italy), Gregorio
Falqui (SISSA/ISAS, Trieste, Italy), Franco Magri (Dip. di Matematica, Univ.
di Milano, Italy), and Marco Pedroni (Dip. di Matematica, Univ. di Genova,
Italy) | Darboux Coverings and Rational Reductions of the KP Hierarchy | 16 pages, LaTeX | null | null | SISSA 131/96/FM | solv-int nlin.SI | null | We use the method of Darboux coverings to discuss the invariant submanifolds
of the KP equations, presented as conservation laws in the space of monic
Laurent series in the spectral parameter (the space of the Hamiltonian
densities). We identify a special class of these submanifolds with the rational
invariant submanifolds entering matrix models of $2D$--gravity, recently
characterized by Dickey and Krichever. Four examples of the general procedure
are provided.
| 2008-02-03 |
solv-int/9610003 | Andrey V. Tsiganov | A.V. Tsiganov | Automorphisms of sl(2) and dynamical r-matrices | 14 pages, Latex | null | null | null | solv-int hep-th math.QA nlin.SI q-alg | null | Two outer automorphisms of infinite-dimensional representations of $sl(2)$
algebra are considered. The similar constructions for the loop algebras and
yangians are presented. The corresponding linear and quadratic $R$-brackets
include the dynamical $r$-matrices.
| 2008-02-03 |
solv-int/9610004 | Parma | N.A. Gromov, I.V. Kostyakov and V.V. Kuratov | Contractions of Integrable Equations | 6 pages, LaTeX, submitted to Proceedings of ' II International
Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12
July,1996), to be published in Int.J.Mod.Phys | null | 10.1142/S0217751X97000256 | null | solv-int nlin.SI | null | The contraction is applied to obtaining of integrable systems associated with
nonsemisimple algebras. The effect of contraction is splitting off some
components from initial system without loss of integrability.
| 2009-10-30 |
solv-int/9610005 | Kenichi Maruno | K. Maruno, K. Kajiwara, S. Nakao, M. Oikawa | Bilinearization of Discrete Soliton Equations and Singularity
Confinement | 14 pages, LaTex | null | 10.1016/S0375-9601(97)00171-0 | null | solv-int nlin.SI | null | Bilinear forms for some nonlinear partial difference equations(discrete
soliton equations) are derived based on the results of singularity confinement.
Using the bilinear forms, the N-soliton and algebraic solutions of the discrete
potential mKdV equation are constructed.
| 2016-09-08 |
solv-int/9610006 | Mts | Andrey Yu. Boldin and Ruslan A. Sharipov (Baskir State University,
Math. Department, Russia) | On the solution of normality equations for the dimension $n\geq 3$ | AmS-TeX, amsppt style, 18 pages | null | null | null | solv-int nlin.SI | null | The normality equations for the Newtonian dynamical systems on an arbitrary
Riemannian manifold of the dimension $n \geq 3$ are considered. Locally the
solution of such equations reduces to three possible cases: in two of them the
solution is written out explicitly, and in the third case the equations of
normality are reduced to an ordinary differential equation of the second order.
Some new examples of explicit solutions of normality equations are constructed.
| 2008-02-03 |
solv-int/9610007 | Robert Conte | R. Conte (CEA Saclay), M. Musette (VUB Brussels) | A new method to test discrete Painlev\'e equations | 12 pages, no figure, standard Latex, to appear in Physics Letters A | null | 10.1016/S0375-9601(96)00783-9 | S96/032 | solv-int nlin.SI | null | Necessary discretization rules to preserve the Painlev\'e property are
stated. A new method is added to the discrete Painlev\'e test, which perturbs
the continuous limit and generates infinitely many no-log conditions.
| 2009-10-30 |
solv-int/9610008 | Wenxiu Ma | Wen-Xiu Ma and Fu-Kui Guo | Lax Representations and Zero Curvature Representations by Kronecker
Product | 9 pages, Latex, to appear in Intern. J. Theoret. Phys | null | 10.1007/BF02435889 | null | solv-int nlin.SI | null | It is showed that Kronecker product can be applied to construct not only new
Lax representations but also new zero curvature representations of integrable
models. Meantime a different characteristic between continuous and discrete
zero curvature equations is pointed out.
| 2009-10-30 |
solv-int/9610009 | Jan de Gier | Jan de Gier and Bernard Nienhuis (University of Amsterdam, The
Netherlands) | The exact solution of an octagonal rectangle triangle random tiling | 26 pages, LaTeX, including 5 figures, to appear in J. Stat. Phys | J. Stat. Phys. 87 (1997) 415-437 | 10.1007/BF02181494 | ITFA 96-35 | solv-int cond-mat nlin.SI | null | We present a detailed calculation of the recently published exact solution of
a random tiling model possessing an eight-fold symmetric phase. The solution is
obtained using Bethe Ansatz and provides closed expressions for the entropy and
phason elastic constants. Qualitatively, this model has the same features as
the square-triangle random tiling model. We use the method of P. Kalugin, who
solved the Bethe Ansatz equations for the square-triangle tiling, which were
found by M. Widom.
| 2015-06-26 |
solv-int/9610010 | Kakei Saburo | Saburo Kakei | An orthogonal basis for the $B_N$-type Calogero model | 9 pages, LaTeX, no figures, several errors are corrected, Appendix is
added | null | null | null | solv-int cond-mat hep-th math.QA nlin.SI q-alg | null | We investigate algebraic structure for the $B_N$-type Calogero model by using
the exchange-operator formalism. We show that the set of the Jack polynomials
whose arguments are Dunkl-type operators provides an orthogonal basis.
| 2008-02-03 |
solv-int/9610011 | Atsuo Kuniba | Zengo Tsuboi (Univ. of Tokyo, Komaba) | Solutions of Discretized Affine Toda Field Equations for A_{n}^{(1)},
B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)} | 22 pages, no figure, LaTeX: Introduction, Summary and Discussion are
revised. (e-mail: ss57058@hongo.ecc.u-tokyo.ac.jp) | J.Phys.Soc.Jap. 66 (1997) 3391-3398 | 10.1143/JPSJ.66.3391 | null | solv-int hep-th nlin.SI | null | It is known that a family of transfer matrix functional equations, the
T-system, can be compactly written in terms of the Cartan matrix of a simple
Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra
with that of an affine Lie algebra, and then we obtain a system of functional
equations different from the T-system. It may be viewed as an X_{n}^{(a)} type
affine Toda field equation on discrete space time. We present, for A_{n}^{(1)},
B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}, its
solutions in terms of determinants or Pfaffians.
| 2009-10-30 |
solv-int/9610012 | null | J. T. Liu and D. F. Wang | Integrabilities of the long range t-J model of twisted boundary
condition | preprint of Rockefeller-ETH, submitted to PRB rapid communication | null | 10.1103/PhysRevB.55.R3344 | null | solv-int cond-mat nlin.SI | null | The integrability of the one-dimensional long range supersymmetric t-J model
has previously been established for both open systems and those closed by
periodic boundary conditions through explicit construction of its integrals of
motion. Recently the system has been extended to include the effect of magnetic
flux, which gives rise to a closed chain with twisted boundary conditions.
While the t-J model with twisted boundary conditions has been solved for the
ground state and full energy spectrum, proof of its integrability has so far
been lacking. In this letter we extend the proof of integrability of the long
range supersymmetric t-J model and its SU(m|n) generalization to include the
case of twisted boundary conditions.
| 2016-09-08 |
solv-int/9610013 | Nalini Joshi | Nalini Joshi and Johannes A. Petersen | Complex Blow-Up in Burgers' Equation: an Iterative Approach | 11 pages in LaTeX. To appear in Bull. Aust. Math. Soc | null | null | null | solv-int nlin.SI | null | We show that for a given holomorphic noncharacteristic surface S in
two-dimensional complex space, and a given holomorphic function on S, there
exists a unique meromorphic solution of Burgers' equation which blows up on S.
This proves the convergence of the formal Laurent series expansion found by the
Painlev\'e test. The method used is an adaptation of Nirenberg's iterative
proof of the abstract Cauchy-Kowalevski theorem.
| 2008-02-03 |
solv-int/9611001 | Nalini Joshi | Rod Halburd and Nalini Joshi | The Coalescence Limit of the Second Painlev\'E Equation | 16 pages in LaTeX (1 figure included) | Stud. Appl. Math. 97 (1996) 1--15 | null | null | solv-int nlin.SI | null | In this paper, we study a well known asymptotic limit in which the second
Painlev\'e equation (P_II) becomes the first Painlev\'e equation (P_I). The
limit preserves the Painlev\'e property (i.e. that all movable singularities of
all solutions are poles). Indeed it has been commonly accepted that the movable
simple poles of opposite residue of the generic solution of P_{II} must
coalesce in the limit to become movable double poles of the solutions of P_I,
even though the limit naively carried out on the Laurent expansion of any
solution of P_{II} makes no sense. Here we show rigorously that a coalescence
of poles occurs. Moreover we show that locally all analytic solutions of P_I
arise as limits of solutions of P_{II}.
| 2008-02-03 |
solv-int/9611002 | null | V.V.Konotop (University of Madeira, Portugal), M. Salerno (University
of Salerno, Italy) | Small-amplitude excitations in a deformable discrete nonlinear
Schroedinger equation | 18 pages (RevTex), 13 figures available upon request | null | 10.1103/PhysRevE.55.4706 | null | solv-int nlin.SI | null | A detailed analysis of the small-amplitude solutions of a deformed discrete
nonlinear Schr\"{o}dinger equation is performed. For generic deformations the
system possesses "singular" points which split the infinite chain in a number
of independent segments. We show that small-amplitude dark solitons in the
vicinity of the singular points are described by the Toda-lattice equation
while away from the singular points are described by the Korteweg-de Vries
equation. Depending on the value of the deformation parameter and of the
background level several kinds of solutions are possible. In particular we
delimit the regions in the parameter space in which dark solitons are stable in
contrast with regions in which bright pulses on nonzero background are
possible. On the boundaries of these regions we find that shock waves and
rapidly spreading solutions may exist.
| 2009-10-30 |
solv-int/9611003 | Alexander V. Razumov | A. V. Razumov, M. V. Saveliev | Some explicit solutions of the Lam\'e and Bourlet type equations | 12 pages, LaTeX file | null | null | LPTENS-96/61 | solv-int dg-ga hep-th math.DG nlin.SI | null | Some special solutions to the multidimensional Lam\'e and Bourlet type
equations are constructed in an explicit form.
| 2008-02-03 |
solv-int/9611004 | null | D. F. Wang | Spinless Calogero-Sutherland model with twisted boundary condition | preprint of ETH-L, appearing in recent PRE | null | 10.1103/PhysRevE.54.4586 | null | solv-int nlin.SI | null | In this work, the spinless Calogero-Sutherland model with twisted boundary
condition is studied. The ground state wavefunctions, the ground state
energies, the full energy spectrum are provided in details.
| 2009-10-30 |
solv-int/9611005 | Jan de Gier | Jan de Gier, Bernard Nienhuis (University of Amsterdam) | On the integrability of the square-triangle random tiling model | 11 pages, LaTeX, inluding 2 postscript figures | Phys. Rev. E 55, 3926 (1997) | 10.1103/PhysRevE.55.3926 | IFTA 96-47 | solv-int cond-mat.stat-mech nlin.SI | null | It is shown that the square-triangle random tiling model is equivalent to an
asymmetric limit of the three colouring model on the honeycomb lattice. The
latter model is known to be the O(n) model at T=0 and corresponds to the
integrable model connected to the affine $A_2^{(1)}$ Lie algebra. Thus it is
shown that the weights of the square-triangle random tiling satisfy the
Yang-Baxter equation, albeit in a singular limit of a more general model. The
three colouring model for general vertex weights is solved by algebraic Bethe
Ansatz.
| 2009-10-30 |
solv-int/9611006 | Denis Uglov | Kouichi Takemura and Denis Uglov | The orthogonal eigenbasis and norms of eigenvectors in the Spin
Calogero-Sutherland Model | 35 pages, AMSLaTeX | null | 10.1088/0305-4470/30/10/039 | RIMS-1114 | solv-int hep-th math.QA nlin.SI q-alg | null | Using a technique based on the Yangian Gelfand-Zetlin algebra and the
associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of
eigenvectors in the Calogero-Sutherland Model with spin, and derive
product-type formulas for norms of these eigenvectors.
| 2009-10-30 |
solv-int/9611007 | YuKui. Zhou | Y.-K. Zhou and K. D. Schotte | The L-Matrix for the Massive Thirring Model | 10 pages, no ps figures, Tex file | Phys Rev D 47 (1993) R1281-R1284 | 10.1103/PhysRevD.47.R1281 | null | solv-int nlin.SI | null | As the new results for the massive Thirring model the L-matrix and the
algebraic relations for its action angle variables are given. So it is shown
most directly that this model which describes self-interacting relativistic
Fermions in one-dimensional space is a quantum integrable system.
| 2009-10-30 |
solv-int/9611008 | Andrei Mal'tsev | A.Ya. Maltsev | The conservation of the Hamiltonian structures in Whitham's method of
averaging | 39 pages, some improvement, corrected misprints | Izvestiya, Mathematics 63:6 (1999), 1171-1201 | null | null | solv-int hep-th nlin.SI | null | The work is devoted to the proof of the conservation of local
field-theoretical Hamiltonian structures in Whitham's method of averaging. The
consideration is based on the procedure of averaging of local Poisson bracket,
proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of
restriction of the Poisson bracket on the submanifold in the functional space,
it is shown in the generic case that the Poisson bracket, constructed by method
of Dubrovin and Novikov, satisfies the Jacobi identity. Besides that, the
invariance of this bracket with respect to the choice of the set of local
conservation laws, used in this procedure, is proved.
| 2008-02-03 |
solv-int/9612001 | Uwe Grimm | Uwe Grimm | Representations of Two-Colour BWM Algebras and Solvable Lattice Models | 6 pages, LaTeX, heron2e.sty (included), Poster presented at GROUP21 | Proceedings of the Quantum Group Symposium at the XXI
International Colloquium on Group Theoretical Methods in Physics, edited by
H.-D. Doebner and V.K. Dobrev, Heron Press, Sofia (1997), pp. 114-119 | null | null | solv-int nlin.SI | null | Many of the known solutions of the Yang-Baxter equation, which are related to
solvable lattice models of vertex- and IRF-type, yield representations of the
Birman-Wenzl-Murakami algebra. From these, representations of a two-colour
generalization of the Birman-Wenzl-Murakami algebra can be constructed, which
in turn are used to derive trigonometric solutions to the Yang-Baxter equation.
In spirit, this construction resembles the fusion procedure, in the sense that
starting from known solutions of the Yang-Baxter equation new solutions can be
obtained.
| 2008-02-03 |
solv-int/9612002 | Nicolai Kitanine | N.M. Bogoliubov, A.G. Izergin, N.A. Kitanine | Correlators of the phase model | LaTeX, 7 pages, One reference has been changed | null | 10.1016/S0375-9601(97)00326-5 | ENSLAPP-L-622/96, HU-TFT-96-41 | solv-int nlin.SI | null | We introduce the phase model on a lattice and solve it using the algebraic
Bethe ansatz. Time-dependent temperature correlation functions of phase
operators and the "darkness formation probability" are calculated in the
thermodynamical limit. These results can be used to construct integrable
equations for the correlation functions and to calculate there asymptotics.
| 2009-10-30 |