一类微分-差分方程的非古典对称分析  

Nonclassical symmetry analysis of a class of differential-difference equations

作　　者：李文婷[1] 蒋鲲[1] 李滨滨 LI Wenting;JIANG Kun;LI Binbie(School of Mathematical Sciences,Heilongjiang University,Harbin 130082,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨130080

出　　处：《黑龙江大学自然科学学报》2020年第2期144-148,共5页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究项目(12541609);黑龙江省高校基本科研业务费黑龙江大学专项资金资助项目(HDRCCX-201615);黑龙江大学教育教学改革工程项目(2017C64)。

摘　　要：本文提出了用于求解非线性微分-差分方程的对称的微分-差分非古典对称法。应用非古典对称法分别得到了两类Toda晶格方程的决定方程,从而求得这两类Toda晶格方程的非古典对称以及相应的约化方程。与古典微分-差分Lie对称方法相比,非古典微分-差分对称方法不需要寻找方程的不变条件及不变解,因此可以使得运算更加便捷。同时该方法得到的对称形式更加丰富,从而可以获得微分-差分方程更多形式的解。In this paper,a differential-difference non-classical symmetry method is proposed to solve some kinds of differential-difference equations.This method is applied to two kinds of Toda lattice equations.The determining equations of the two equations are obtained by using the non-classical symmetry method.As a result,the corresponding non-classical symmetry and reduction equation are obtained.Comparing with the classical differential-difference Lie symmetry method,the differential-difference non-classical symmetry method does not need the invariant conditions and the invariant solutions of the equation.It makes the operations more convenient and the forms of symmetries are more abundant,and also more solutions of the differential-difference equations are obtained.

关 键 词：微分-差分方程 非古典对称方法 (2+1)维Toda-like方程 Lie对称分析 

分 类 号：O175.75[理学—数学]