symmetry and perturbation of the vector nonlinear schrodinger equation abstract we show that the symmetry algebra of the n component vector nonlinear schrodinger nls equation is given by the loop algebra of su n u 1 the recursion operator and the virasoro type algebra of the master symmetries suitable for any n or even for an operator nls equation are also constructed we have shown that a general su n invariant third order correction of the vector nls equation can be moved in the next order of perturbation theory i e the corresponding normal form of the equation is shown to be integrable

backlund transformation in bilinear form for a higher order nonlinear schrodinger equation backlund transformation in bilinear form is presented for a higher order nonlinear schrodinger equation which describes the propagation of ultrashort light pulses in optical fibers with symbolic computation and starting from the backlund transformation the analytical soliton solution is obtained from a trivial solution and the inverse scattering transform scheme is also derived furthermore the n soliton solution in double wronskian form is given and the value of the arbitrary constant appearing in the backlund transformation is determined for a transformation between the n 1 and n soliton solutions the results obtained from the backlund transformation might be valuable in optical communications

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

equivalence relations on separated nets arising from linear toral flows in 1998 burago kleiner and mcmullen independently proved the existence of separated nets in r which are not bi lipschitz equivalent bl to a lattice a finer equivalence relation than bl is bounded displacement bd separated nets arise naturally as return times to a section for minimal r actions we analyze the separated nets which arise via these constructions focusing particularly on nets arising from linear r actions on tori we show that generically these nets are bl to a lattice and for some choices of dimensions and sections they are generically bd to a lattice we also show the existence of such nets which are not bd to a lattice

soliton solutions of the kadomtsev petviashvili ii equation we study a general class of line soliton solutions of the kadomtsev petviashvili ii kpii equation by investigating the wronskian form of its tau function we show that in addition to the previously known line soliton solutions of kpii this class also contains a large variety of multisoliton solutions many of which exhibit nontrivial spatial interaction patterns we also show that in general such solutions consist of unequal numbers of incoming and outgoing line solitons from the asymptotic analysis of the tau function we explicitly characterize the incoming and outgoing line solitons of this class of solutions we illustrate these results by discussing several examples

bright n soliton solutions in terms of the triple wronskian for the coupled nonlinear schrodinger equations in optical fibers the coupled nonlinear schrodinger nls equations are usually used to describe the dynamics of two component solitons in optical fibers via the darboux transformation the coupled nls equations of the manakov type are found to have triple wronskian solutions proof is finished by virtue of some new triple wronskian identities by solving the zero potential lax pair the triple wronskian solutions give the bright n soliton solutions which are characterized by 3n complex parameters to obtain an understanding of the asymptotic behavior of the bright n soliton solutions with arbitrary n some algebraic properties of the triple wronskian are analyzed and an algebraic procedure is presented to derive the explicit expressions of the asymptotic solitons as t

an extension of the wronskian technique for the multicomponent wronskian solution to the vector nonlinear schrodinger equation in this paper the wronskian technique is applied to the vector nonlinear schrodinger equation with arbitrary m components which arises from some applications in the multimode fibers photorefractive materials and bose einstein condensates via the iterative algorithm based on the darboux transformation the m 1 component wronskian solution is generated from the zero solution the verification of the solution is finished by using the m 1 component wronskian notation and new determinantal identities with a set of n linearly independent solutions of the zero potential lax pair the m 1 component wronskian solution is found to be the representation of the bright n soliton solution which contains m 1 n parameters for characterizing the asymptotic behavior of the generic bright n soliton solution an algebraic procedure is derived to obtain the explicit expressions of asymptotic solitons as t

entire majorants via euler maclaurin summation it is the aim of this article to give extremal majorants of type 2 for the class of functions f n x sgn x x n where n n as applications we obtain positive definite extensions to r of it m defined on r 1 1 where m n optimal bounds in hilbert type inequalities for the class of functions it m and majorants of type 2 for functions whose graphs are trapezoids

extremal functions in de branges and euclidean spaces ii this paper presents the gaussian subordination framework to generate optimal one sided approximations to multidimensional real valued functions by functions of prescribed exponential type such extremal problems date back to the works of beurling and selberg and provide a variety of applications in analysis and analytic number theory here we majorize and minorize on bbb r n the gaussian bf x mapsto e pi lambda bf x 2 where lambda0 is a free parameter by functions with distributional fourier transforms supported on euclidean balls optimizing weighted l 1 errors by integrating the parameter lambda against suitable measures we solve the analogous problem for a wide class of radial functions applications to inequalities and periodic analogues are discussed the constructions presented here rely on the theory of de branges spaces of entire functions and on new interpolation tools derived from the theory of laplace transforms of laguerre p o lya functions

on a variable coefficient korteweg de vries model in fluid filled elastic tubes in this paper we investigate a variable coefficient korteweg de vries vckdv model in arterial mechanics a new lax pair of the vckdv model is constructed based on which the b cklund transformation solitonic and some other solutions of the vckdv model are obtained with symbolic computation the influence of the variable coefficients on solitonic propagation is investigated based on the solitonic solution which has the following three aspects i the coefficient of the nonlinear term affects the solitonic amplitude ii the coefficient of the dispersive term controls the solitonic velocity and propagation trace iii the coefficient of the dissipative term acts on both the solitonic amplitude and the velocity we also analyze the variations of velocity and pressure of blood flow along the scaled axial coordinate after the static deformation in the vicinity of stenosis

interpolation formulas with derivatives in de branges spaces ii abstract we investigate necessary and sufficient conditions under which entire functions in de branges spaces can be recovered from function values and values of derivatives our main focus is on spaces with a structure function whose logarithmic derivative is bounded in the upper half plane

negaton and positon solutions of the kdv and mkdv hierarchy we give a systematic classification and a detailed discussion of the structure motion and scattering of the recently discovered negaton and positon solutions of the korteweg de vries hierarchy there are two distinct types of negaton solutions which we label and where n 1 is the order of the wronskian used in the derivation for negatons the number of singularities and zeros is finite and they show very interesting time dependence the general motion is in the positive x direction except for certain negatons which exhibit one oscillation around the origin in contrast there is just one type of positon solution which we label for positons one gets a finite number of singularities for n odd but an infinite number for even values of n the general motion of positons is in the negative x direction with periodic oscillations negatons and positons retain their identities in a scattering process and their phase shifts are discussed we obtain a simple explanation of all phase shifts by generalizing the notions of mass and centre of mass to singular solutions finally it is shown that negaton and positon solutions of the kdv hierarchy can be used to obtain corresponding new solutions of the modified kdv hierarchy

state transformations of colliding optical solitons and possible application to computation in bulk media using explicit bright soliton solutions for the coupled manakov system recently described by radhakrishnan lakshmanan and hietarinta we show that collisions of these solitons can be completely described by explicit linear fractional transformations of a complex valued polarization state we design sequences of solitons operating on other sequences of solitons that effect logic operations including controlled not gates both data and logic operators have the self restoring and reusability features of digital logic circuits this suggests a method for implementing computation in a bulk nonlinear medium without interconnecting discrete components

bell polynomial approach and n soliton solution for the extended lotka volterra equation in plasmas symbolically investigated in this paper is the extended lotka volterra elv equation which can govern the kinetics of the discrete peaks of the weak langmuir turbulence in plasmas without the linear damping and random noise binary bell polynomials are applied to the bilinearization of the discrete system bilinear backlund transformation of the elv equation is constructed n soliton solution in terms of the extended casorati determinant is also presented and verified propagation and interaction behaviors of the langmuir turbulence are analyzed it is demonstrated that the number of the interacting langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting langmuir waves

the vector nonlinear schrodinger hierarchy abstract an article published recently by one of the authors jne presents closed form solutions for zero curvature representations of the vector nonlinear schrodinger hierarchy several of these results are confirmed computationally but left unproven in this article we begin by providing strict algebraic proofs of these results the forms of the hierarchy s associated spectral curves are investigated and proven to have only odd genus without the introduction of integration constants we admit specific non zero constants of integration to the hierarchy and show that even genus curves may be introduced in a very straightforward manner thereby accessing the full family of finite gap solutions to the vector nonlinear schrodinger equation finally an original construction of the infinite set of conserved densities of the hierarchy is given

investigation on a nonisospectral fifth order korteweg de vries equation generalized from fluids in this paper a nonisospectral fifth order korteweg de vries equation generalized from fluids is investigated with symbolic computation such equation is transformed into its bilinear form through a proposed dependent variable transformation with one more parameter than those in the existing literature n soliton solutions backlund transformation and lax pair in the explicit forms are constructed based on the above results the characteristic line method is applied to discuss the features of the solitons for the nonisospectral problem i e the controllable solitonic velocities and widths four types of solitonic structures with the different solitonic velocities widths amplitudes and backgrounds are also illustrated

exact soliton solutions of coupled nonlinear schrodinger equations shape changing collisions logic gates and partially coherent solitons the different dynamical features underlying soliton interactions in coupled nonlinear schrodinger equations which model multimode wave propagation under varied physical situations in nonlinear optics are studied in this paper by explicitly constructing multisoliton solutions up to four soliton solutions for two coupled and arbitrary n coupled nonlinear schrodinger equations using the hirota bilinearization method we bring out clearly the various features underlying the fascinating shape changing intensity redistribution collisions of solitons including changes in amplitudes phases and relative separation distances and the very many possibilities of energy redistributions among the modes of solitons however in this multisoliton collision process the pairwise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons detailed asymptotic analysis also shows that when solitons undergo multiple collisions there exists the exciting possibility of shape restoration of at least one soliton during interactions of more than two solitons represented by three and higher order soliton solutions from an application point of view we have shown from the asymptotic expressions how the amplitude intensity redistribution can be written as a generalized linear fractional transformation for the n component case also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters leading to possible multistate logic in addition we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions thereby explaining their variable profile and shape variation in collision process

time dependent fiber bundles with local load sharing ii general weibull fibers fiber bundle models fbms are useful tools in understanding failure processes in a variety of material systems while the fibers and load sharing assumptions are easily described fbm analysis is typically difficult monte carlo methods are also hampered by the severe computational demands of large bundle sizes which overwhelm just as behavior relevant to real materials starts to emerge for large size scales interest continues in idealized fbms that assume either equal load sharing els or local load sharing lls among fibers rules that reflect features of real load redistribution in elastic lattices the present work focuses on a one dimensional bundle of n fibers under lls where life consumption in a fiber follows a power law in its load with exponent ensuremath rho and integrated over time this life consumption function is further embodied in a functional form resulting in a weibull distribution for lifetime under constant fiber stress and with weibull exponent ensuremath beta thus the failure rate of a fiber depends on its past load history except for ensuremath beta 1 we develop asymptotic results validated by monte carlo simulation using a computational algorithm developed in our previous work phys rev e 63 021507 2001 that greatly increases the size n of treatable bundles e g 10 6 fibers in 10 3 realizations in particular our algorithm is mathcal o n text text ln text n in contrast with former algorithms which were mathcal o n 2 making this investigation possible regimes are found for ensuremath beta ensuremath rho pairs that yield contrasting behavior for large n for ensuremath rho g1 and large n brittle weakest volume behavior emerges in terms of characteristic elements groupings of fibers derived from critical cluster formation and the lifetime eventually goes to zero as n ensuremath rightarrow ensuremath infty unlike els which yields a finite limiting mean for 1 2 ensuremath le ensuremath rho ensuremath le 1 however lls has remarkably similar behavior to els appearing to be virtually identical for ensuremath rho 1 with an asymptotic gaussian lifetime distribution and a finite limiting mean for large n the coefficient of variation follows a power law in increasing n but except for ensuremath rho 1 the value of the negative exponent is clearly less than 1 2 unlike in els bundles where the exponent remains 1 2 for 1 2l ensuremath rho ensuremath le 1 for sufficiently small values 0l ensuremath rho 1 a transition occurs depending on ensuremath beta whereby lls bundle lifetimes become dominated by a few long lived fibers thus the bundle lifetime appears to approximately follow an extreme value distribution for the longest lived of a parallel group of independent elements which applies exactly to ensuremath rho 0 the lower the value of ensuremath beta the higher the transition value of ensuremath rho below which such extreme value behavior occurs no evidence was found for limiting gaussian behavior for ensuremath rho g1 but with 0l ensuremath beta ensuremath rho 1 l1 as might be conjectured from quasistatic bundle models where ensuremath beta ensuremath rho 1 mimics the weibull exponent for fiber strength

bounding s t and s_1 t on the riemann hypothesis let pi s t denote the argument of the riemann zeta function zeta s at the point s frac 1 2 it assuming the riemann hypothesis we present two proofs of the bound begin aligned s t le left frac 1 4 o 1 right frac log t log log t end aligned for large t this improves a result of goldston and gonek by a factor of 2 the first method consists of bounding the auxiliary function s 1 t int 0 t s u text d u using extremal functions constructed by carneiro littmann and vaaler we then relate the size of s t to the size of the functions s 1 t pm h s 1 t when h asymp 1 log log t the alternative approach bounds s t directly relying on the solution of the beurling selberg extremal problem for the odd function f x arctan left frac 1 x right frac x 1 x 2 this draws upon recent work by carneiro and littmann

inverse scattering transform for the vector nonlinear schrodinger equation with nonvanishing boundary conditions the inverse scattering transform for the vector defocusing nonlinear schrodinger nls equation with nonvanishing boundary values at infinity is constructed the direct scattering problem is formulated on a two sheeted covering of the complex plane two out of the six jost eigenfunctions however do not admit an analytic extension on either sheet of the riemann surface therefore a suitable modification of both the direct and the inverse problem formulations is necessary on the direct side this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions the discrete spectrum bound states and symmetries of the direct problem are then discussed in the most general situation a discrete eigenvalue corresponds to a quartet of zeros poles of certain scattering data the inverse scattering problem is formulated in terms of a generalized riemann hilbert rh problem in the upper lower half planes of a suitable uniformization variable special soliton solutions are constructed from the poles in the rh problem and include dark dark soliton solutions which have dark solitonic behavior in both components as well as dark bright soliton solutions which have one dark and one bright component the linear limit is obtained from the rh problem and is shown to correspond to the fourier transform solution obtained from the linearized vector nls system

darboux transformation for a two component derivative nonlinear schrodinger equation in this paper we consider a two component derivative nonlinear schrodinger equation and present a simple darboux transformation for it by iterating this darboux transformation we construct a compact representation for the n soliton solutions

hilbert spaces and the pair correlation of zeros of the riemann zeta function montgomery s pair correlation conjecture predicts the asymptotic behavior of the function n t defined to be the number of pairs and of ordinates of nontrivial zeros of the riemann zetafunction satisfying 0 0 using montgomery s formula and some extremal functions of exponential type these functions are optimal in the sense that they majorize and minorize the characteristic function of the interval in a way to minimize the l1 r 1 sin x x 2 dx error we give a complete solution for this extremal problem using the framework of reproducing kernel hilbert spaces of entire functions this extends previous work of p x gallagher 18 in 1985 where the case 1 2 n was considered using non extremal majorants and minorants

soliton like solutions of a generalized variable coefficient higher order nonlinear schrodinger equation from inhomogeneous optical fibers with symbolic computation for the long distance communication and manufacturing problems in optical fibers the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable coefficient nonlinear schrodinger equation with higher order effects such as the third order dispersion self steepening and self frequency shift in this paper we firstly determine the general conditions for this equation to be integrable by employing the painleve analysis based on the obtained 3 3 lax pair we construct the darboux transformation for such a model under the corresponding constraints and then derive the nth iterated potential transformation formula by the iterative process of darboux transformation through the one and two soliton like solutions we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers

a damage model based on failure threshold weakening abstract a variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions involving either critical phenomena or spinodal nucleation here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding we introduce a failure threshold weakening parameter into the cellular automaton slider block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event we show that a critical point is reached beyond which the probability of a system wide event scales with this weakening parameter we provide a mapping to the percolation transition and show that the values of the scaling exponents approach the values for mean field percolation spinodal nucleation as lattice size l is increased for fixed r we also examine the effect of the weakening parameter on the frequency magnitude scaling relationship and the ergodic behavior of the model

casorati determinant solution for the relativistic toda lattice equation the relativistic toda lattice equation is decomposed into three toda systems the toda lattice itself backlund transformation of toda lattice and discrete time toda lattice it is shown that the solutions of the equation are given in terms of the casorati determinant by using the casoratian technique the bilinear equations of toda systems are reduced to the laplace expansion form for determinants the n soliton solution is explicitly constructed in the form of the casorati determinant

the use of backlund transformations in obtaining n soliton solutions in wronskian form the wronskian formulation of the n soliton solutions of various nonlinear evolution equations modified korteweg de vries with both zero and non zero asymptotic conditions sine gordon korteweg de vries kadomtsev petviashvili and boussinesq equations are obtained by inductive use of backlund transformations in hirota s 1980 bilinear notation

soliton solutions backlund transformation and wronskian solutions for the extended 2 1 dimensional konopelchenko dubrovsky equations in fluid mechanics abstract this paper is to investigate the extended 2 1 dimensional konopelchenko dubrovsky equations which can be applied to describing some phenomena in the stratified shear flow the internal and shallow water waves and plasmas bilinear form equations are transformed from the original equations and n soliton solutions are derived via symbolic computation bilinear form backlund transformation and single soliton solution are obtained and illustrated wronskian solutions are constructed from the backlund transformation and single soliton solution

painleve analysis and integrability of coupled non linear schrodinger equations considering a system of coupled non linear schrodinger nls equations the authors discuss the integrability properties through painleve p analysis for the two coupled nls equations they show that there exists a pair of parametric values possessing the p property for which the associated backlund transformation bt and the hirota bilinearisation are constructed these parametric choices are identical to those of zakharov and schulman 1982 who established the integrability in terms of motion invariants finally they extend the p analysis to the n coupled nls system and identify two parametric choices possessing the p property which are natural generalisations of the two coupled nls cases

pair correlation estimates for the zeros of the zeta function via semidefinite programming abstract in this paper we study the distribution of the non trivial zeros of the riemann zeta function s and other l functions using montgomery s pair correlation approach we use semidefinite programming to improve upon numerous asymptotic bounds in the theory of s including the proportion of distinct zeros counts of small gaps between zeros and sums involving multiplicities of zeros

extremal functions in de branges and euclidean spaces abstract in this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on r n these extremal functions minimize the l 1 r n x 2 2 n d x distance to the original function where 1 is a free parameter to achieve this result we develop new interpolation tools to solve an associated extremal problem for the exponential function f x e x where 0 in the general framework of de branges spaces of entire functions we then specialize the construction to a particular family of homogeneous de branges spaces to approach the multidimensional euclidean case finally we extend the result from the exponential function to a class of subordinated radial functions via integration on the parameter 0 against suitable measures applications of the results presented here include multidimensional versions of hilbert type inequalities extremal one sided approximations by trigonometric polynomials for a class of even periodic functions and extremal one sided approximations by polynomials for a class of functions on the sphere s n 1 with an axis of symmetry

n fold darboux transformation and solitonic interactions of a variable coefficient generalized boussinesq system in shallow water abstract under consideration in this paper is a variable coefficient generalized boussinesq system for the long weakly nonlinear and weakly dispersive surface waves in shallow water with the aid of symbolic computation n fold darboux transformation n dt is constructed for that system analytic solutions of the system are obtained via the n dt elastic interactions of three bell shaped and periodic bell shaped solitons are obtained fusion interactions and periodic fusion fission interactions of the solitary waves are graphically analyzed which are inelastic

on the backlund gauge transformation and homoclinic orbits of a coupled nonlinear schrodinger system abstract the backlund gauge transformation for a system of coupled nls nonlinear schrodinger equations with a degenerate associated spectral operator is derived from an algebraic perspective extending aspects of other results m boiti tu guizhang il nuovo cimento 71b 1982 253 264 d h sattinger v d zurkowski physica d 26 1 3 1987 225 250 that apply in the context of non degenerate spectral operators moreover we demonstrate how the backlund gauge transformation can be used to explicitly construct the entire unstable manifold via superpositions of homoclinic orbits of a plane wave solution with both self phase instabilities and coupling instabilities this work builds on the results of ercolani et al n ercolani m g forest d w mclaughlin physica d 18 1986 472 474 n ercolani m g forest d w mclaughlin physica d 43 2 3 1990 349 384 for the sine gordon equation and forest et al m g forest d w mclaughlin d j muraki o c wright j nonlinear sci in press m g forest s p sheu o c wright phys lett a in press for the integrable coupled nls system

a class of extremal functions for the fourier transform we determine a class of real valued integrable functions f x and corresponding functions m x such that f x 1 and the value of mfo is miimi several applications of these functions to number theory and analysis are given

gaussian subordination for the beurling selberg extremal problem we determine extremal entire functions for the problem of ma jorizing minorizing and approximating the gaussian function e x 2 by en tire functions of exponential type the combination of the gaussian and a general distribution approach provides the solution of the extremal problem for a wide class of even functions that includes most of the previously known examples for instance 3 4 10 and 17 plus a variety of new interesting functions such asjxj for 1 log x 2 2 x 2 2 for 0 log x2 2 andx2n logx2 forn2 n further applications to number theory include optimal approximations of theta functions by trigonometric polynomi als and optimal bounds for certain hilbert type inequalities related to the discrete hardy littlewood sobolev inequality in dimension one

extremal problems in de branges spaces the case of truncated and odd functions in this paper we find extremal one sided approximations of exponential type for a class of truncated and odd functions with a certain exponential subordination these approximations optimize the l 1 mathbb r e x 2 mathrm d x error where e is an arbitrary hermite biehler entire function of bounded type in the upper half plane this extends the work of holt and vaaler duke math j 83 203 247 1996 for the signum function we also provide periodic analogues of these results finding optimal one sided approximations by trigonometric polynomials of a given degree to a class of periodic functions with exponential subordination these extremal trigonometric polynomials optimize the l 1 mathbb r mathbb z mathrm d vartheta error where vartheta is an arbitrary nontrivial measure on mathbb r mathbb z the periodic results extend the work of li and vaaler indiana univ math j 48 1 183 236 1999 who considered this problem for the sawtooth function with respect to jacobi measures our techniques are based on the theory of reproducing kernel hilbert spaces of entire functions and of polynomials and on the construction of suitable interpolations with nodes at the zeros of laguerre polya functions

gauge theory of ba cklund transformations ii abstract a class of gauge transformations is constructed for hamiltonian hierarchies of completely integrable systems on semi simple lie algebras these transformations create or annihilate poles in the scattering data hence create or annihilate solitons in the potential q in that sense they generalize backlund transformations to which they reduce precisely for the 2 2 akns systems to each backlund gauge transformation is associated an automorphism in the weyl group of the lie algebra two proofs are given to show that these backlund gauge transformations preserve the nonlinear evolution equation one proof uses the transformation of the scattering data under the backlund transformation the second proof is purely gauge theoretic

soliton solutions to the 3rd nonisospectral akns system abstract bilinear form of the nonisospectral akns equation is given the n soliton solutions and double wronskian solution are obtained through hirota s direct method and wronskian technique respectively the nonisospectral mkdv equation and its multi soliton solutions are presented by reducing

soliton solutions of the korteweg de vries and the kadomtsev petviashvili equations the wronskian technique the well known soliton solutions of the kadomtsev petviashvili equations are written in terms of determinants of wronskian form by using this compact representation together with the hirota bilinear form of the equations it is demonstrated by elementary algebraic methods that the n soliton solution satisfies the evolution equation and the n and n 1 soliton solutions satisfy the associated backlund transformation the relation of these results to the eigensolutions of the inverse scattering method and to the more usual representation of the n soliton solution is also given

n soliton solutions for the 2 1 dimensional hirota maccari equation in fluids plasmas and optical fibers abstract under investigation in this paper is the hirota maccari equation which is a generalized 2 1 dimensional model in fluid dynamics plasma physics and optical fiber communication with the aid of the hirota bilinear method and symbolic computation the corresponding n soliton solutions are given and illustrated the characteristic face method and asymptotic analysis are applied to discuss the solitonic propagation and collision including the bidirectional solitons elastic interactions and inelastic interactions finally a kind of special phenomenon with the parameters varying is investigated which might provide people with useful information on the dynamics of the relevant fields

time to failure of dynamic local load sharing fiber bundle models in 1 to 3 dimensions abstract extensive monte carlo simulations are carried out in one two and three dimensions for dynamic local load sharing fiber bundle models following a power law breaking rule with exponent this exponent controls the degree of disorder of the bundle the results are obtained using two methods of introducing disorder in the simulations in the standard or classical monte carlo method the disorder is quenched in the second or radioactive method the disorder is annealed both methods give identical mean time to failure values for systems of the same size however the radioactive method proves to be more efficient due to the smaller standard deviation of the probability distribution function of the time to failure we take advantage of this efficiency to compute the asymptotic mean time to failure of large systems as a function of the degree of disorder as parameterized by based on these extensive simulations conclusions are drawn regarding the upper critical dimension of time dependent local load sharing fiber bundle models

a note on the zeros of zeta and l functions let pi s t denote the argument of the riemann zeta function at the point s tfrac 1 2 it assuming the riemann hypothesis we give a new and simple proof of the sharpest known bound for s t we discuss a generalization of this bound for a large class of l functions including those which arise from cuspidal automorphic representations of gl m over a number field we also prove a number of related results including bounding the order of vanishing of an l function at the central point and bounding the height of the lowest zero of an l function

the n soliton solutions for the non isospectral mkdv equation the bilinear form of the non isospectral mkdv equation is given and the exact n soliton solutions are obtained through hirota method and wronskian technique respectively c

some extremal functions in fourier analysis ii we obtain extremal majorants and minorants of exponential type for a class of even functions on which includes log x and x where 1 1 we also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree as applications we obtain optimal estimates for certain hermitian forms which include discrete analogues of the one dimensional hardy littlewood sobolev inequalities a further application provides an erdos turan type inequality that estimates the sup norm of algebraic polynomials on the unit disc in terms of power sums in the roots of the polynomials

solitonic propagation and interaction for a generalized variable coefficient forced korteweg de vries equation in fluids under investigation is a generalized variable coefficient forced korteweg de vries equation in fluids and other fields from the bilinear form of such equation the n soliton solution and a type of analytic solution are constructed with symbolic computation analytic analysis indicates that 1 dispersive and dissipative coefficients affect the solitonic velocity 2 external force term affects the solitonic velocity and background 3 line damping coefficient and some parameters affect the solitonic velocity background and amplitude solitonic propagation and interaction can be regarded as the combination of the effects of various variable coefficients according to a constraint among the nonlinear dispersive and line damping coefficients in this paper the possible applications of our results in the real world are also discussed in three aspects i e solution with the constraint solution without the constraint and approximate solution

solitonic interactions and double wronskian type solutions for a variable coefficient variant boussinesq model in the long gravity water waves abstract under investigation in this paper is a variable coefficient variant boussinesq vcvb model for the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth connection between the vcvb model and a variable coefficient ablowitz kaup newell segur system is revealed under certain constraints with the help of the symbolic computation multi solitonic solutions in terms of the double wronskian determinant for the vcvb model are derived interactions among the vcvb solitons are discussed a novel dynamic property is observed i e the coexistence of elastic inelastic interactions