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.

本文研究的是一个相对论 Toda 晶格系统，其中一个扰动参数α被 Suris缩写为 RTL_( α ) 系统，它可以描述晶格中粒子通过指数相互作用力相互作用的运动。首先，构建了一个与RTL_( α )系统相关的可积格子层次，从中研究了一些相关的可积性质，如哈密顿结构、刘维尔可积性和守恒定律。其次，构造离散广义 ( m , 2 N − m )-折叠 Darboux 变换以推导出多孤子解、高阶有理和半有理解以及它们的 RTL_(α ) 系统。通过图形和渐近分析来分析孤子弹性相互作用和有理解的细节。最后，通过数值模拟研究了孤子动力学演化，表明小噪声对孤子传播的影响很小。这些结果可能为 RTL_( α ) 系统描述的非线性晶格动力学提供新的见解。