Integrability,multi-soliton and rational solutions,and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter

• 作者: Meng-Li Qin Xiao-Yong Wen Cui-Lian Yuan
• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: MATHEMATICAL PHYSICS
• 页码范围: 13-42
• 页数: 30页
• 语种: 英文

摘要

Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameter α abbreviated as RTL_(α)system by Suris,which may describe the motions of particles in lattices interacting through an exponential interaction force.First of all,an integrable lattice hierarchy associated with an RTL_(α)system is constructed,from which some relevant integrable properties such as Hamiltonian structures,Liouville integrability and conservation laws are investigated.Secondly,the discrete generalized(m,2N-m)-fold Darboux transformation is constructed to derive multi-soliton solutions,higher-order rational and semi-rational solutions,and their mixed solutions of an RTL_(α)system.The soliton elastic interactions and details of rational solutions are analyzed via the graphics and asymptotic analysis.Finally,soliton dynamical evolutions are investigated via numerical simulations,showing that a small noise has very little effect on the soliton propagation.These results may provide new insight into nonlinear lattice dynamics described by RTL_(α)system.