非线性反应扩散方程组的符号不变量和变量分离解

Sign-invariant and Separation of Variables Solutions of the System of Nonlinear Reaction-diffusion Equations

主要利用Galaktionov提出的符号不变量的方法来研究非线性反应扩散方程组的精确解,首先引入Hamilton-Jacobi算子作为方程组的符号不变量,通过对称约化找到方程组容许的超定方程组系统并对其求解,进而得到了允许符号不变量的方程组的具体形式、约束条件和其变量分离解,最后给出某些例子.

This paper is devoted to the quasilinear partial differential equations by study on the exact solutions for the systems of the method of the sign-invariant theory, which is introduced by Galaktionov. We Introduce the Hamilton-Jacobi operator as the sign-invariant of the nonlinear reaction-diffusion systems. As a conseqhence, we present overdetermined nonlinear system by symmetry reduction. Finally we obtain some explicit solutions of the corresponding systems and give some examples.