一类(2+1)维微分差分方程的对称分类

A symmetry classification of (2+1) dimensional differential-difference equation

基于Lie点对称提出了一个对称分类算法用于构造一类(2+1)维微分差分方程的对称及Lie代数结构。计算该(2+1)维方程的Lie点对称,以及函数F_n的分类方程和允许变换,将(2+1)维微分差分方程的对称问题转化成构造分类方程的所有可能解问题,并根据该(2+1)维方程的生成元的标准形式以及其对应的分类方程,得到不变量方程的显示形式以及该(2+1)维方程的一维Lie代数。

In this work we have proposed a symmetry classification algorithm of(2+1) dimensional differential-difference equation according to the intrinsic Lie point symmetries, allowed trans-formations and Lie algebraic structures. Firstly, we compute the intrinsic Lie point symmetries of the equation together with the classifying equation for F_n and the allowed transformations admitted by the equation. After that, based on the fact that the explicit forms of the commutation relations define the low-dimensional abstract Lie algebras, we describe all the inequivalent realizations of symmetry algebras by the basis operators. By inserting the canonical forms of symmetry generators into the classified equations and solving them, the explicit forms of invariant equations are derived.