一类非线性晶格方程的非古典对称分析

Nonclassical symmetry analysis of a type of nonlinear lattice equations

本文提出了获得微分差分方程对称的非古典对称方法。非古典对称方法在无穷小变换之后增加了一个限制条件,即不变表面条件。通过求解满足该条件的控制方程组,得到相应的约化方程,这样就可以得到微分差分方程的非古典对称。该方法避免了无穷小生成元延拓的繁琐计算,使得对称的形式更加丰富,从而可以得到微分差分方程更多形式的解。以(2+1)维Toda-like晶格方程为例,应用非古典对称方法得到其相应的对称及约化方程。

The nonclassical symmetry method of differential-difference equation is proposed.Comparing with the classical Lie symmetry method,a constraint condition which is called the invariant surface condition is added to the infinitesimal transformation in this method.By solving the governing equations and the corresponding reduced equations,the nonclassical symmetry of the differential-difference equation can be obtained.This method avoids the tedious calculation of infinitesimal generators’s extension.Meanwhile the form of symmetries form is more abundant.At last,the determining equations,the correspon-ding symmetries and the reduced equations of the(2+1)-dimensional Toda-like lattice equation are obtained by this nonclassical symmetry method.