Integrability, discrete kink multi-soliton solutions on an inclined plane background and dynamics in the modified exponential Toda lattice equation

2021 ◽  
Author(s):  
Cui-Lian Yuan ◽  
Xiao-Yong Wen
Keyword(s):  
Toda Lattice ◽  
Soliton Solutions ◽  
Lattice Equation ◽  
Inclined Plane ◽  
Toda Lattice Equation

Multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation via Hirota’s bilinear method

2014 ◽  
Vol 92 (3) ◽  
pp. 184-190 ◽  
Author(s):  
Sheng Zhang ◽  
Dong Liu
Keyword(s):  
Variable Coefficient ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Hirota’S Bilinear Method ◽  
Lattice Equation ◽  
Bilinear Method ◽  
Dimensional Variable ◽  
Toda Lattice Equation ◽  
Multisoliton Solutions

In this paper, Hirota’s bilinear method is extended to construct multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation. As a result, new and more general one-soliton, two-soliton, and three-soliton solutions are obtained, from which the uniform formula of the N-soliton solution is derived. It is shown that Hirota’s bilinear method can be used for constructing multisoliton solutions of some other nonlinear differential-difference equations with variable coefficients.

scholarly journals Tropical limit of matrix solitons and entwining Yang–Baxter maps

2020 ◽  
Vol 110 (11) ◽  
pp. 3015-3051
Author(s):  
Aristophanes Dimakis ◽  
Folkert Müller-Hoissen
Keyword(s):  
Soliton Solution ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Baxter Equation ◽  
Kp Equation ◽  
Lattice Equation ◽  
Soliton Interactions ◽  
The Matrix ◽  
Tropical Limit ◽  
Toda Lattice Equation

Abstract We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter equation together with the Yang–Baxter map. Such maps have been called “entwining Yang–Baxter maps” in recent work. In fact, the map of polarizations obtained from a pure 2-soliton solution of a matrix KP equation, and already for the matrix KdV reduction, is not in general a Yang–Baxter map, but it is described by one of the two maps or their inverses. We clarify why the weaker version of the Yang–Baxter equation holds, by exploring the pure 3-soliton solution in the “tropical limit,” where the 3-soliton interaction decomposes into 2-soliton interactions. Here, this is elaborated for pure soliton solutions, generated via a binary Darboux transformation, of matrix generalizations of the two-dimensional Toda lattice equation, where we meet the same entwining Yang–Baxter maps as in the KP case, indicating a kind of universality.

N-SOLITON SOLUTIONS AND CONSERVATION LAWS OF THE MODIFIED TODA LATTICE EQUATION

2012 ◽  
Vol 26 (06) ◽  
pp. 1150032 ◽  
Author(s):  
XIAO-YONG WEN
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Lax Representation ◽  
Lattice Equation ◽  
Interaction Behavior ◽  
Toda Lattice Equation

The modified Toda lattice equation is investigated via Darboux transformation (DT) technique, the N-fold DT is constructed based on its Lax representation. The N-soliton solutions are also derived via the resulting N-fold DT. Soliton structures and interaction behavior of those solutions are shown graphically. Finally, the infinitely many conservation laws for that system are given.

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