Two new integrable differential-difference hierarchies related to the relativistic Toda lattice equation and their soliton fusion or fission

Hongyan Wang; Guoqing Zhu

doi:10.1142/S0217984922500087

Two new integrable differential-difference hierarchies related to the relativistic Toda lattice equation and their soliton fusion or fission

Hongyan Wang
, Guoqing Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Starting from a discrete spectral problem, two new integrable differential-difference hierarchies are presented and their Lax pairs are given, respectively. The first hierarchy is related to the relativistic Toda lattice equation. Darboux transformations for the first systems in the two hierarchies are derived, respectively, accordingly their explicit solutions are obtained. By selecting appropriate parameters, we can see the phenomena of soliton fission or soliton fusion.

Original language	English
Article number	2250008
Journal	Modern Physics Letters B
Volume	36
Issue number	9
DOIs	https://doi.org/10.1142/S0217984922500087
Publication status	Published - 30 Mar 2022

Keywords

Darboux transformation
Discrete spectral problem
differential-difference hierarchy
soliton fission and fusion

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10.1142/S0217984922500087

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abstract = "Starting from a discrete spectral problem, two new integrable differential-difference hierarchies are presented and their Lax pairs are given, respectively. The first hierarchy is related to the relativistic Toda lattice equation. Darboux transformations for the first systems in the two hierarchies are derived, respectively, accordingly their explicit solutions are obtained. By selecting appropriate parameters, we can see the phenomena of soliton fission or soliton fusion.",

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AU - Wang, Hongyan

AU - Zhu, Guoqing

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N2 - Starting from a discrete spectral problem, two new integrable differential-difference hierarchies are presented and their Lax pairs are given, respectively. The first hierarchy is related to the relativistic Toda lattice equation. Darboux transformations for the first systems in the two hierarchies are derived, respectively, accordingly their explicit solutions are obtained. By selecting appropriate parameters, we can see the phenomena of soliton fission or soliton fusion.

AB - Starting from a discrete spectral problem, two new integrable differential-difference hierarchies are presented and their Lax pairs are given, respectively. The first hierarchy is related to the relativistic Toda lattice equation. Darboux transformations for the first systems in the two hierarchies are derived, respectively, accordingly their explicit solutions are obtained. By selecting appropriate parameters, we can see the phenomena of soliton fission or soliton fusion.

KW - Darboux transformation

KW - Discrete spectral problem

KW - differential-difference hierarchy

KW - soliton fission and fusion

UR - https://www.scopus.com/pages/publications/85128399042

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DO - 10.1142/S0217984922500087

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Two new integrable differential-difference hierarchies related to the relativistic Toda lattice equation and their soliton fusion or fission

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Keywords

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