偏微分方程约化的精确定义
A precise definition of reduction of partial differential equations
摘要：
我们给出了一个全面的分析对称性（经典和非经典）减少偏微分方程的现代理论的基本概念之间的相互关系。使用介绍的定义减少微分方程，我们建立等价的非经典（条件对称性）和直接（Angloman）的方法减少偏微分方程。作为例子，我们给出了（1+3）维非线性波方程的非经典约化。条件对称的方法时，适用于方程的问题产生了一些非李的减少，这是深远的推广众所周知的对称减少的非线性波方程。
英文摘要：
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yields a number of non-Lie reductions which are far-reaching generalization of the well-known symmetry reductions of the nonlinear wave equations.
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