相关论文: Complexiton Solutions of the Toda Lattice Equation
A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a…
The relativistic Toda lattice equation is decomposed into three Toda systems, the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete time Toda lattice. It is shown that the solutions of the equation are given in…
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…
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…
It is shown that the $N$-dark soliton solutions of the integrable discrete nonlinear Schr\"odinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the…
We construct $N$-soliton solution for the non-autonomous discrete-time Toda lattice equation, which is a generalization of the discrete-time Toda equation such that the lattice interval with respect to time is an arbitrary function in time.
We use the generalized Cauchy matrix approach to derive the N-soliton solutions for the (2+2)-dimensional Toda lattice.
A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda…
In this work, for an equation of high even order with a fractional derivative in the sense of Caputo, a problem is studied in a rectangular domain with conjugation conditions. A criterion for the uniqueness of a solution is given. The…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…
Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the $\tau$ functions for the Painlev\'e equations is also discussed.
In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions.…
We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various…
We consider the soliton solutions in 1- and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota's method. We explicitly construct the solutions satisfying…
We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions.…
The delay Lotka-Volterra and delay Toda lattice equations are delay-differential extensions of the well-known soliton equations, the Lotka-Volterra and Toda lattice equations, respectively. This paper investigates integrable properties of…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources are established and solved. Two families of quasideterminant solutions are presented for the non-Abelian two-dimensional Toda lattice…