摘要:
本文把离散的Lie点对称群分析方法应用于一个非线性微分–差分Toda晶格方程(即Toda-like晶格方程)。即首先应用Lie点对称方法约化Toda晶格方程，用以得到此方程对应的超定方程，再引入一个约化条件解超定方程，从而对该Toda晶格方程进行了相似约化，进而得到了其新的精确解。
Abstract: In this paper, the discrete Lie point symmetry group analysis method is applied on a nonlinear dif- ferential-difference Toda lattice equation (i.e. a Toda-like equation), i.e. firstly, the Toda lattice equation is reduced by using Lie point symmetry to get the overdetermined equations corresponding to this Toda lattice equation, then a conditional symmetry is introduced to solve the overdetermined equations, so the similarity reduction for the Toda lattice equation is obtained, and then the new exact solutions of this Toda lattice equa- tion are obtained.