the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

partial classification of modules for the algebra of skew derivations over the d dimensional torus for the algebra of skew derivations over a torus we classify the irreducible weight modules with some restrictions

maximum norm error estimates of a linear cadi method for the klein gordon schrodinger equations abstract in this paper an efficient linear compact alternating direction implicit cadi scheme with second order temporal accuracy and fourth order spatial accuracy is proposed for approximating solution to the initial boundary problem for the two dimensional klein gordon schrodinger equations furthermore maximum norm error estimates of numerical solutions are obtained by using the energy method and the mathematical induction method finally some numerical experiments are presented to support the theoretical results

modules of highest weight type for the algebra of derivations over a rational quantum torus for the lie algebra of derivations over a rational quantum torus we construct a class of irreducible weight modules with all finite dimensional weight spaces which are called the modules of highest weight type generating the notion for the case of commutative torus for the lie algebra of derivations over a rational quantum torus we construct a class of irreducible weight modules with all finite dimensional weight spaces which are called the modules of highest weight type generating the notion for the case of commutative torus

regular article a fast spectral algorithm for nonlinear wave equations with linear dispersion spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains including well known cases such as the korteweg de vries and nonlinear schrodinger equations for the best computational efficiency one needs also to use high order methods in time while somehow bypassing the usual severe stability restrictions we use linearly implicit multistep methods with the innovation of choosing different methods for different ranges in fourier space high accuracy at low wavenumbers and a stability at high wavenumbers this new approach compares favorably to alternatives such as split step and integrating factor or linearly exact methods

two numerical meshless techniques based on radial basis functions rbfs and the method of generalized moving least squares gmls for simulation of coupled klein gordon schrodinger kgs equations in the present study three numerical meshless methods are being considered to solve coupled klein gordon schrodinger equations in one two and three dimensions first the time derivative of the mentioned equation will be approximated using an implicit method based on crank nicolson scheme then kansa s approach rbfs pseudo spectral ps method and generalized moving least squares gmls method will be used to approximate the spatial derivatives the proposed methods do not require any background mesh or cell structures so they are based on a meshless approach applying three techniques reduces the solution of the one two and three dimensional partial differential equations to the solution of linear system of algebraic equations as is well known the use of kansa s approach makes the coefficients matrix in the above linear system of algebraic equations to be ill conditioned and we applied lu decomposition technique but when we employ ps method fasshauer 2007 the matrix of coefficients in the obtained linear system of algebraic equations is well conditioned also the gmls technique yields a well conditioned linear system because a shifted and scaled polynomial basis will be used at the end of this paper we provide some examples on one two and three dimensions for obtaining numerical simulations also the obtained numerical results show the applicability of the proposed three methods to find the numerical solution of the kgs equations

efficient and accurate numerical methods for the klein gordon schrodinger equations in this paper we present efficient unconditionally stable and accurate numerical methods for approximations of the klein gordon schrodinger kgs equations with without damping terms the key features of our methods are based on i the application of a time splitting spectral discretization for a schrodinger type equation in kgs ii the utilization of fourier pseudospectral discretization for spatial derivatives in the klein gordon equation in kgs iii the adoption of solving the ordinary differential equations odes in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying crank nicolson leap frog for linear nonlinear terms for time derivatives the numerical methods are either explicit or implicit but can be solved explicitly unconditionally stable and of spectral accuracy in space and second order accuracy in time moreover they are time reversible and time transverse invariant when there is no damping terms in kgs conserve or keep the same decay rate of the wave energy as that in kgs without or with a linear damping term keep the same dynamics of the mean value of the meson field and give exact results for the plane wave solution extensive numerical tests are presented to confirm the above properties of our numerical methods for kgs finally the methods are applied to study solitary wave collisions in one dimension 1d as well as dynamics of a 2d problem in kgs

a note on the g g expansion method abstract we demonstrate that the g g expansion method which is often used in finding exact solutions of nonlinear differential equation is equivalent to the well known tanh method and application of these methods gives the same exact solutions of nonlinear differential equations

irreducible witt modules from weyl modules and gln modules abstract for an irreducible module p over the weyl algebra k n resp k n and an irreducible module m over the general linear lie algebra gl n using shen s monomorphism we make p m into a module over the witt algebra w n resp over w n we obtain the necessary and sufficient conditions for p m to be an irreducible module over w n resp w n and determine all submodules of p m when it is reducible thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non weight modules over w n and w n including some known modules and many new modules

numerical simulation of interaction between schrodinger field and klein gordon field by multisymplectic method abstract we propose a multisymplectic scheme to solve the coupled klein gordon schrodinger system the scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law and can simulate the original waves well in a long time this scheme also has discrete quasi norm conservation law numerical experiments demonstrate the consistency between the theoretical analysis and the numerical results

central and noncentral extensions of multi graded lie algebras the author constructs noncentral extensions of the algebras of vector fields and gauge transformations in n dimensional space in one dimension they reduce to the ordinary central extensions occurring in virasoro and kac moody algebras

integrable representations for generalized virasoro toroidal lie algebras abstract in this paper we give the structure of irreducible integrable modules of generalized virasoro toroidal lie algebras with finite dimensional weight spaces and non zero central charge

lowest energy representations of non centrally extended diffeomorphism algebras we describe a class of non central extensions of the diffeomorphism algebra in n dimensional spacetime and construct lowest energy modules thereof thus generalizing work of eswara rao and moody there is one representation for each representation of an extension of the semi direct product similar modules are constructed for gauge algebras

differential equations in vertex algebras and simple modules for the lie algebra of vector fields on a torus we study irreducible representations for the lie algebra of vector fields on a 2 dimensional torus constructed using the generalized verma modules we show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the lie algebra of vector fields we prove this result by studying vertex algebras associated with the lie algebra of vector fields on a torus and solving non commutative differential equations that we derive using the vertex algebra technique

exact solutions to the two dimensional korteweg de vries burgers equation two methods are described for obtaining exact travelling monotone shock wave solutions to the two dimensional korteweg de vries burgers equation they are compared with two methods that have been reported recently by other authors

classification of category j modules for divergence zero vector fields on a torus abstract we consider a category of modules that admit compatible actions of the commutative algebra of laurent polynomials and the lie algebra of divergence zero vector fields on a torus and have a weight decomposition with finite dimensional weight spaces we classify indecomposable and irreducible modules in this category

finite difference method for generalized zakharov equations abstract a conservative difference scheme is presented for the initial boundary value problem for generalized zakharov equations the scheme canbe implicit or semiexplicit depending on the choice of a parameter on thebasis of a priori estimates and an inequality about norms convergence of thedifference solution is proved in order 0 h2 t2 which is better than previous results introductionthe zakharov equations 20 1 1 iet exx ne 0 1 2 ntt n e 2 xx 0describe the propagation of langmuir waves in plasmas here the complexunknown function e is the slowly varying envelope of the highly oscillatoryelectric field and the unknown real function n denotes the fluctuation of the ion density about its equilibrium value the global existence of a weak solution for the zakharov equations in one dimension is proved in 19 and existence and uniqueness of a smooth solutionfor the equations are obtained provided smooth initial data are prescribed numerical methods for the zakharov equations are studied only in 5 9 10

symmetry reductions and similarity solutions of the 3 1 dimensional breaking soliton equation abstract using the compatibility method we obtain three types of symmetry of the 3 1 dimensional breaking soliton equation by solving the corresponding characteristic equations associated with symmetry equations symmetry reductions of the 3 1 dimensional breaking soliton equation are given first then some special types of similarity solutions are constructed

application of rational expansion method for stochastic differential equations abstract by means of the hermite transformation a new general ansatz and the symbolic computation system maple we apply the riccati equation rational expansion method 24 to uniformly construct a series of stochastic non traveling wave solutions for stochastic differential equations to illustrate the effectiveness of our method we take the stochastic mkdv equation as an example and successfully construct some new and more general solutions the method can also be applied to solve other nonlinear stochastic differential equation or equations

exact solutions of some systems of nonlinear partial differential equations using symbolic computation abstract in this paper we present a solution method that utilizes symbolic computation to obtain exact traveling wave solutions of some systems of nonlinear partial differential equations the solution method is demonstrated by obtaining solutions to the variant shallow water wave equations

a class of conservative orthogonal spline collocation schemes for solving coupled klein gordon schrodinger equations abstract a class of discrete time orthogonal spline collocation schemes for solving coupled klein gordon schrodinger equations with initial and boundary conditions are considered these schemes are constructed by using piecewise cubic hermite interpolations in space combined with finite difference methods in time it is proved that the schemes have the conservation laws of discrete energy and possess second order accuracy in maximum norm and fourth order in l 2 norm for time and space respectively the conservation laws and rate of convergence are verified in numerical experiments moreover the propagations of solitary waves and collisions of two head on solitary waves are also well simulated

partial classification of modules for lie algebra of diffeomorphisms of d dimensional torus we consider the lie algebra of the group of diffeomorphisms of a d dimensional torus which is also known to be the algebra of derivations on a laurent polynomial ring a in d commuting variables denoted by der a the universal central extension of der a for d 1 is the so called virasoro algebra the connection between virasoro algebra and physics is well known see for example the book on conformal field theory by di francesco mathieu and senechal in this paper we classify a der a modules which are irreducible and have finite dimensional weight spaces earlier larsson constructed a large class of modules the so called tensor fields based on gld modules which are also a modules we prove that they exhaust all a der a irreducible modules

exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid exact travelling wave solutions in terms of the weierstrass p function of the equation eta t a0 eta x a1 eta eta x a2 eta xxx b0 eta xx b 1 eta eta x x b2 eta xxxx 0 are obtained these solutions may describe particularly both the evolution of a bounded conoidal wave and kink shaped waves

parametric spline schemes for the coupled nonlinear schrodinger equation abstract in this study the parametric cubic spline scheme is implemented to find the approximate solution of the coupled nonlinear schrodinger equations this scheme is based on the crank nicolson method in time and parametric cubic spline functions in space the error analysis and stability of the scheme are investigated and the numerical results show that we can get different precision schemes by choosing suitably parameter values and this scheme is unconditionally stable two problems are solved to illustrate the efficiency of the methods as well as to compare with other methods

irreducible representations for toroidal lie algebras abstract in this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal lie algebras to accomplish this we develop a general theory of z n graded lie algebras with polynomial multiplication we construct modules by the standard inducing procedure and study their irreducible quotients using the vertex operator technics

partial classification of cuspidal simple modules for virasoro like algebra abstract let p be the lie algebra of hamiltonian vector fields on the torus which is also known as the virasoro like algebra a special kind of the so called block type lie algebra and let a be the laurent polynomial algebra in two variables in this paper by following s e rao s strategy of backward induction we prove that any quasi finite simple a p module has to come from larsson shen s construction

high order linear compact conservative method for the nonlinear schrodinger equation coupled with the nonlinear klein gordon equation abstract in this paper we design a linear compact conservative numerical scheme which preserves the original conservative properties to solve the klein gordon schrodinger equation the proposed scheme is based on using the finite difference method the scheme is three level and linear implicit priori estimate and the convergence of the finite difference approximate solutions are discussed by the discrete energy method numerical results demonstrate that the present scheme is conservative efficient and of high accuracy

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

approximate solutions to the zakharov equations via finite differences abstract an energy preserving linearly implicit finite difference scheme is presented for computing solutions to the periodic initial value problem for the zakharov equations solitary waves and colliding solitary waves are computed and a comparison is made with previous calculations

optimal point wise error estimate of a compact difference scheme for the klein gordon schrodinger equation abstract in this paper we propose a compact finite difference scheme for computing the klein gordon schrodinger equation kgse with homogeneous dirichlet boundary conditions the proposed scheme not only conserves the total mass and energy in the discrete level but also is linearized in practical computation except for the standard energy method a new technique is introduced to obtain the optimal convergent rate without any restriction on the grid ratios at the order of o h 4 2 in the l norm with time step and mesh size h finally numerical results are reported to test the theoretical results

generalized riccati equation rational expansion method and its application by directly extending the riccati equation rational expansion method a new method is developed for constructing a series of exact analytical solutions of an averaged dispersion managed fiber system equation adme including some new rational formal soliton like solutions triangle like solutions and rational solutions

classification of irreducible bounded weight modules over the derivation lie algebras of quantum tori abstract let d 1 be an integer q q i j d d a d d complex matrix satisfying q i i 1 q i j q j i 1 with all q i j being roots of unity let c q be the rational quantum torus algebra associated with q and der c q its derivation lie algebra in this paper we give a complete classification of irreducible bounded weight modules over der c q they turn out to be irreducible sub quotients of der c q module v v w for a finite dimensional irreducible gl d module v a finite dimensional graded irreducible gl n module w and c d where the integer n is uniquely determined by q

the irreducible modules for the derivations of the rational quantum torus abstract let c q be the quantum torus associated with the d d matrix q q i j where q i j are roots of unity with q i i 1 and q i j 1 q j i for all 1 i j d let der c q be the lie algebra of all the derivations of c q in this paper we define the lie algebra der c q c q and classify its irreducible modules with finite dimensional weight spaces these modules under certain conditions turn out to be of the form v c q where v is a finite dimensional irreducible g l d module

analysis of a conservative high order compact finite difference scheme for the klein gordon schrodinger equation abstract in this paper we propose and analyze a conservative high order compact finite difference scheme for the klein gordon schrodinger kgs equation with dirichlet boundary condition by introducing the time derivative of one solution as a separate dependent variable we rewrite the kgs equation as a system of partial differential equations pdes and obtain a two level compact finite difference scheme based on the energy method and matrix knowledge on the vector form we convert the point wise form of the proposed compact scheme into an equivalent vector form and analyze its conservative and convergence properties we prove that the proposed scheme preserves the total energy and charge in the discrete forms and the convergence rate of the scheme without any restrictions on the grid ratio is at the order of o h 4 2 in l 2 norm where h and are spatial and temporal steps respectively numerical experiments are carried out to verify the performance of the scheme

on time splitting spectral approximations for the schrodinger equation in the semiclassical regime in this paper we study time splitting spectral approximations for the linear schrodinger equation in the semiclassical regime where the planck constant e is small in this regime the equation propagates oscillations with a wavelength of o e and finite difference approximations require the spatial mesh size h o e and the time step k o e in order to obtain physically correct observables much sharper mesh size constraints are necessary for a uniform l2 approximation of the wave function the spectral time splitting approximation under study will be proved to be unconditionally stable time reversible and gauge invariant it conserves the position density and gives uniform l2 approximation of the wave function for k o e and h o e extensive numerical examples in both one and two space dimensions and analytical considerations based on the wigner transform even show that weaker constraints e g k independent of e and h o e are admissible for obtaining correct observables finally we address the application to nonlinear schrodinger equations and conduct some numerical experiments to predict the corresponding admissible meshing strategies

exp function method for the exact solutions of fifth order kdv equation and modified burgers equation abstract in this paper we implemented the exp function method for the exact solutions of the fifth order kdv equation and modified burgers equation by using this scheme we found some exact solutions of the above mentioned equations

a unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations a unified basic frame of rational expansion methods is presented which leads to closed form solutions of nonlinear evolution equations nlees the new unified algorithms are given to find exact rational formal polynomial solutions of nlees in terms of jacobi elliptic functions solutions of the riccati equation and solutions of the generalized riccati equation they can be implemented in symbolic computation system maple as applications of the methods we choose some physical significance nlees to illustrate the methods as a consequence we not only can successfully obtain the solutions found by most existing jacobi elliptic function methods and tanh methods but also find other new and more general solutions at the same time

numerical comparison of five difference schemes for coupled klein gordon schrodinger equations in quantum physics in this paper we compare the classical conservative properties of five difference schemes applied to the coupled klein gordon schr odinger equations in quantum physics and investigate the numerical behaviour of the schemes in the implementation numerical results reveal merits and shortcomings of the schemes and show that all five schemes are stable in the classical conservation laws in the sense of preservation of classical conservative properties conservative schemes are better than others

integrable modules for twisted toroidal extended affine lie algebras abstract in this paper we classify the irreducible integrable modules for the twisted toroidal extended affine lie algebras twisted toroidal eala in short with finite dimensional weight spaces when the finite dimensional center acts non trivially using an automorphism we reduce to the case where k 0 acts non trivially and k i 1 i n act trivially twisted toroidal eala has a natural triangular decomposition and we prove that any irreducible integrable module of it with finite dimensional weight spaces is a highest weight module with respect to the above triangular decomposition the highest weight space is an irreducible module for the zeroth component of the twisted toroidal eala we then describe the highest weight space in detail

spectral method for solving the system of equations of schro dinger klein gordon field in this paper we construct the conservative spectral scheme for the periodic initial value problem for a system of equations of the complex schrodinger field interacting with the real klein gordon field and estimate the error which is xv gf nk nn xv xv nk ixnn xv 1 o k2 n 1

explicit multi symplectic methods for klein gordon schrodinger equations in this paper we propose explicit multi symplectic schemes for klein gordon schrodinger equation by concatenating suitable symplectic runge kutta type methods and symplectic runge kutta nystrom type methods for discretizing every partial derivative in each sub equation it is further shown that methods constructed in this way are multi symplectic and preserve exactly the discrete charge conservation law provided appropriate boundary conditions in the aim of the commonly practical applications a novel 2 order one parameter family of explicit multi symplectic schemes through such concatenation is constructed and the numerous numerical experiments and comparisons are presented to show the efficiency and some advantages of the our newly derived methods furthermore some high order explicit multi symplectic schemes of such category are given as well good performances and efficiencies and some significant advantages for preserving the important invariants are investigated by means of numerical experiments

convergence of an energy preserving scheme for the zakharov equations in one space dimension an energy preserving linearly implicit finite difference scheme is presented for approximating solutions to the periodic cauchy problem for the one dimensional zakharov system of two nonlinear partial differential equations first order convergence estimates are obtained in a standard energy norm in terms of the initial errors and the usual discretization errors

efficient and stable numerical methods for the generalized and vector zakharov system we present efficient and stable numerical methods for approximations of the generalized zakharov system gzs and vector zakharov system for multicomponent plasma vzsm with without a linear damping term the key points in the methods are based on i a time splitting discretization of a schrodinger type equation in gzs or vzsm ii discretizing a nonlinear wave type equation by a pseudospectral method for spatial derivatives and iii solving the ordinary differential equations odes in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying crank nicolson leap frog for linear nonlinear terms for time derivatives the methods are explicit unconditionally stable and of spectral order accuracy in space and second order accuracy in time moreover they are time reversible and time transverse invariant when there is no damping term in gzs or vzsm conserve or keep the same decay rate of the wave energy as that in gzs or vzsm without a or with a linear damping term and give exact results for the plane wave solution extensive numerical tests are presented for plane waves and solitary wave collisions in one dimensional gzs and we also give the dynamics of three dimensional vzsm to demonstrate our new efficient and accurate numerical methods furthermore the methods are applied to study the convergence and quadratic convergence rates of vzsm to gzs and of gzs to the nonlinear schrodinger nls equation in the subsonic limit regime 0 varepsilon ll1 where the parameter varepsilon is inversely proportional to the acoustic speed our tests also suggest that the following meshing strategy or varepsilon resolution is admissible in this regime spatial mesh size h o varepsilon and time step k o varepsilon

algebras of diffeomorphisms of the n torus the general algebra d n v of infinitesimal diffeomorphisms of the n torus s1 n involving generators lv m depending on a structure vector v cn and a vector valued index m zn is constructed several results are proved for this algebra special cases of the algebra were previously presented in ramos shrock e ramos and r e shrock int j mod phys a 4 4279 1989 the concept of the q rank of the space v of structure vectors denoted rq v is defined and certain related cartan matrices are introduced it is shown that d n v as an ungraded algebra is simple if and only if rq v n i e the q rank of v is maximal a classification under isomorphisms is given for the algebra and is shown to reduce to a classification of the cartan matrices the space of structure vectors is isomorphic to the unique cartan subalgebra a number of properties concerning the central extensions of these algebras are then proved for the case dim v 1 rq v n it is shown that the central extension is unique fo

compact finite difference schemes with high accuracy for one dimensional nonlinear schrodinger equation abstract in this paper two compact finite difference schemes are presented for the numerical solution of the one dimensional nonlinear schrodinger equation the discrete l 2 norm error estimates show that convergence rates of the present schemes are of order o h 4 2 numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy

wn and wn module structures on u hn abstract let h n be the cartan subalgebra of the witt algebras w n der c t 1 t 2 t n and w n der c t 1 1 t 2 1 t n 1 where 1 n in this paper we classify the modules over w n and over w n which are free u h n modules of rank 1 these are the w n modules n a s for some n 1 n c n a c and s 1 2 n and w n modules n a for some n c n and some a c

the cauchy riemann equations on product domains we establish the l 2 theory for the cauchy riemann equations on product domains provided that the cauchy riemann operator has closed range on each factor we deduce regularity of the canonical solution on p 1 forms in special sobolev spaces represented as tensor products of sobolev spaces on the factors of the product this leads to regularity results for smooth data

a conservative numerical scheme for a class of nonlinear schrodinger equation with wave operator in this paper the initial boundary value problem of a class of nonlinear schrodinger equation with wave operator is considered an explicit and efficient finite difference scheme is presented this is a scheme of four levels with a discrete conservative law convergence and stability are proved

a conservative difference scheme for the zakharov equations a new conservative difference scheme is presented for the periodic initial value problem of zakharov equations the scheme can be implicit or semi explicit depending on the choice of a parameter the discretization of the initial condition is of second order accuracy which is consistent with the accuracy of the scheme on the basis of a priori estimates and an inequality about norms convergence of the difference solutions is proved in the energy norm numerical experiments with the schemes are done for several test cases computational results demonstrate that the new semi explicit scheme with a new initial approximation is more accurate and computationally efficient

periodic solutions of the non integrable convective fluid equation in the present paper we have obtained and analyzed a family of exact periodic solutions of the nonlinear evolution partial differential convecting fluid equation cfe by applying a modification of the bilinear transformation method this modification is used in view of the circumstance that cfe is a non integrable nonlinear equation a detailed consideration has been given to the quite important case of balance between the dispersion and nonlinear effects establishing that this balance changes the structure of the equation itself the exact periodic solutions of cfe have been also found in the important case when cfe is identical with the kuramoto sivashinsky equation

error estimates of a conservative finite difference fourier pseudospectral method for the klein gordon schrodinger equation abstract a semi linearized time stepping method based on the finite difference in time and fourier pseudospectral discretization for spatial derivatives is constructed and analyzed for the klein gordon schrodinger equation the resulting numerical scheme is proved to conserve the total mass and energy in the discrete levels the maximum norm error estimates reflecting the second order accuracy in time and spectral accuracy in space are established by using the standard energy method coupled with the induction argument an efficient numerical algorithm is reported to speed up the evaluation of resulting algebra equation by means of the fast discrete fourier transform numerical experiments are presented to show the effectiveness of our method and to confirm our analysis

new families of irreducible weight modules over sl3 abstract let n 1 be an integer c n b c and v a gl n module we define a class of weight modules f b v over sl n 1 using the restriction of modules of tensor fields over the lie algebra of vector fields on n dimensional torus in this paper we consider the case n 2 and prove the irreducibility of such 5 parameter sl 3 modules f b v generically all such modules have infinite dimensional weight spaces and lie outside of the category of gelfand tsetlin modules hence this construction yields new families of irreducible sl 3 modules

exact solutions of multi component nonlinear schrodinger and klein gordon equations applying the sec q tanh q method phys lett a 298 2002 253 we find a class of exact solution of multi component nonlinear schrodinger and klein gordon equations and generalize the correspond results in phys lett a 298 2002 253 and j phys a math gen 34 2001 4281

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

a class of new simple modules for sln 1 and the witt algebra abstract let g sl n 1 w n or w n d i 1 n c t i in this paper we classify the full subcategory d g of g mod consisting of modules which are free of rank 1 when restricted to u d the irreducibility of modules in d g is determined using modules in d sl n 1 we construct classes of modules which are free of finite rank and classes of infinitely generated modules when restricted to the cartan subalgebra

exact solutions of systems describing interacting populations with low critical densities the generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented the exact solutions of nde systems describing the evolution of two interacting populations in two cases both populations have the low critical density or low critical density is typical for only one of populations are obtained

on the weakly nonlinear evolution of a perturbed planar solid liquid interface abstract the linear analysis of a perturbed planar solid liquid interface in a pure substance is carried out with the non equilibrium interface temperature given by a general monotone dependence on the local interface velocity and zero crystalline anisotropy on the basis of rescaling chosen via linear analysis a weakly nonlinear equation of the kuramoto sivashinsky type for the interface dynamics is derived

convergence of a conservative difference scheme for a class of klein gordon schrodinger equations in one space dimension a conservative difference scheme is presented for the initial boundary value problem of a class of klein gordon schrodinger equations the scheme can be implicit or implicit explicit depending on the choice of a parameter on the basis of the priori estimates and an inequality about norms convergence of the difference solution is proved with order o h 2 t 2 in the energy norm

exact solutions of the equation for surface waves in a convecting fluid abstract a method for finding exact solutions and the first integrals is presented the basic idea of the method is to use the value of the fuchs index that appears in the painleve test to construct the auxiliary equation for finding the first integrals and exact solutions of nonlinear differential equations it allows us to obtain the first integrals and new exact solutions of some nonlinear ordinary differential equations the main feature of the method is that we do not assign a solution function at the beginning we find this function during calculations this approach is conceptually equivalent to the third step of the painleve test and sometimes allows us to change this step our approach generalizes a number of other methods for finding exact solutions of nonlinear differential equations we demonstrate a method for finding the traveling wave solutions and the first integrals of the well known nonlinear evolution equation for description of surface waves in a convecting liquid the general solution of this equation at some conditions on parameters and new traveling wave solutions of the fourth order equation are found

extended diffeomorphism algebras and trajectories in jet space let the dro diffeomorphism reparametrization observer algebra dro n be the extension of diff n diff 1 by its four inequivalent virasoro like cocycles here diff n is the diffeomorphism algebra in n dimensional spacetime and diff 1 describes reparametrizations of trajectories in the space of tensor valued p jets dro n has a fock module for each p and each representation of gl n analogous representations for gauge algebras higher dimensional kac moody algebras are also given the reparametrization symmetry can be eliminated by a gauge fixing procedure resulting in previously discovered modules in this process two dro n cocycles transmute into anisotropic cocycles for diff n thus the fock modules of toroidal lie algebras and their derivation algebras are geometrically explained

on tsertsvadze s difference scheme for the kuramoto tsuzuki equation in this paper we have proved the second order convergence in l norm of the tsertsvadze s difference scheme for the kuramoto tsuzuki equation the existence uniqueness and iterative algorithm are also discussed in detail furthermore a l second order convergent linearized difference scheme is given for inhomogeneous equation all results are obtained without any restrictions on the meshsizes at last a numerical example is presented

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

vertex representations for n toroidal lie algebras and a generalization of the virasoro algebra vertex representations are obtained for toroidal lie algebras for any number of variables these representations afford representations of certainn variable generalizations of the virasoro algebra that are abelian extensions of the lie algebra of vector fields on a torus

new solitonic solutions to a 3 1 dimensional jimbo miwa equation abstract performing computerized symbolic computation we are able to present new analytic solutions of a 3 1 dimensional jimbo miwa equation which does not pass any of the conventional integrability tests applying the generalized tanh method we have found such exact solutions as both the nontraveling solitonic and traveling solitary waves

an efficient conservative difference scheme for fractional klein gordon schrodinger equations abstract in the paper we give an efficient conservative scheme for the fractional klein gordon schrodinger equations based on the central difference scheme the crank nicolson scheme and leap frog scheme first we use central difference scheme for discretizing the system in space direction second we use crank nicolson and leap frog scheme for discretizing the system in time direction we find that the scheme can be decoupled linearized and suitable for parallel computation to increase computing efficiency and preserve mass and energy conservation laws the convergence of the scheme is discussed and it is shown that the scheme is of the accuracy o 2 h 2 the numerical experiments are given and verify the correctness of theoretical results and the efficiency of the scheme

irreducible representations of the lie algebra of the diffeomorphisms of ad dimensional torus in this paper we investigate the irreducibility of certain modules for the lie algebra of diffeomorphisms of torus t the lie algebra of diffeomorw 1 1 x phisms can be described as the derivations of a s c t t see 1 d w x w x rss we denote this lie algebra by der a larsson l1 constructed a functor from gl modules to der a modules in this paper we prove that d the image of a finite dimensional irreducible gl module is most often d irreducible the only exceptions are fundamental modules and the onedimensional modules in these cases we describe the sub modules and the quotients surprisingly the same class of modules image of finite dimen w x sional gl module are also constructed in e without any reference to d gl modules they are motivated by the vertex operator constructions in d w x em more details near the end of this introduction we will now describe our results in more detail let gl be the d lie algebras of d d matrices over complex numbers c let gl s sl d d c id where sl is the finite dimensional simple lie algebra of trace zero d matrices and id the identity matrix which is central it is well known that finite dimensional irreducible modules and dominant integral weights are in one one correspondence for a finite dimensional simple lie algebra so let v c be finite dimensional irreducible sl module corresponding to a d dominant integral weight c let id the central element act by a complex number b and denote the corresponding gl module by v c b d a d d larsson defined see 1 6 a functor f for a belonging to c rz from w x gl modules to der a modules in l1 these modules are weight modules d

numerical analysis for fourth order compact conservative difference scheme to solve the 3d rosenau rlw equation in this paper a fourth order compact and energy conservative difference scheme for three dimensional rosenau rlw equation is proposed the scheme is a two level and nonlinear implicit scheme it is proved by the discrete energy method that the compact scheme is solvable the convergence and stability of the difference scheme is obtained and its numerical convergence order is o 2 h4 in the l norm we discuss an iterative algorithm for solving the nonlinear algebraical system generated by the nonlinear compact scheme and prove its convergence numerical experiment results show that the theory is accurate and the method is efficient and reliable

integrable representations for the twisted full toroidal lie algebras the purpose of this work is to classify irreducible integrable modules of the twisted full toroidal lie algebra with finite dimensional weight spaces and non zero central charges there are three families of such modules two of which are classified

condition r and proper holomorphic maps between equidimensional product domains we consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex euclidean space where both source and target can be represented as cartesian products of smoothly bounded domains it is shown that such mappings extend smoothly up to the closures of the domains provided each factor of the source satisfies condition r it also shown that the number of smoothly bounded factors in the source and target must be the same and the proper holomorphic map splits as a product of proper mappings between the factor domains c 2013 elsevier inc all rights reserved

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave