非线性偏微分方程组的广义变量分离解

Generalized separation of variables solutions of a system of nonlinear partial differential equations

在假设不变子空间为二维的前提下,利用不变子空间方法有效构造了一个非线性偏微分方程组所允许的若干二维不变子空间,基于这些不变子空间获得方程组的一系列不同形式的广义变量分离解;同时基于符号计算系统Maple给出相应的符号计算算法,该符号计算方法可以容易地由低维扩展到高维情形.

In terms of the invariant subspace method and under the assumption that the dimension of invariant subspace is two, a number of two-dimensional invariant subspaces are obtained and a series of different separation of variables solutions are given correspondingly. At the same time, the symbolic solving algorithm is given based on the symbolic computation system Maple such that the method can be easily extended from low dimension to high dimension cases.