偏微分方程(组)完全对称分类微分特征列集算法

Differential Characteristic Set Algorithm for the Complete Symmetry Classification of(Partial) Differential Equations

给出了一个确定含参数偏微分方程(组)的完全对称分类微分特征列集算法,该算法能够直接、系统地确定偏微分方程(组)的完全对称分类.用给出的算法获得了含任意函数类参数的线性和非线性波动方程完全势对称分类.这也是微分形式特征列集算法(微分形式吴方法)在微分方程领域中的新应用.

A differential polynomial characteristic set algorithm for the complete symmetry classification of （partial） differential equations with some parameters was given, which made the solution of the complete symmetry classification problem for （partial） differential equations become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary fimction parameter were presented. This is a new application of differential form characteristic set algrithmc （differential form Wu＇s method） in field of differential equations.