非线性Chaffee-Infante反应扩散方程的新精确解

New Exact Solutions of Nonlinear Chafee-Infante Reaction and Diffusion Equation

反应扩散方程描述了物质的输运、扩散和流动等物理过程,其精确解的构建在数学、物理、化学、生物等领域有其重要的应用意义.运用广义的Riccati方程代换法解Chaffee-Infante反应扩散方程,获得了27种形式的解,丰富了精确行波解的形式.推广运用该方法,可以构建其它类型的非线性反应扩散方程的行波解.

Reaction-diffusion equations are mathematical models which explain the processes of transition,diffusion and fluidity of substances.Constructing the exact solutions of this kind of equations are naturally applied in many fields such as mathematics,physics,chemistry and biology.In this paper,by applying the generalized Riccati equation substitution,the exact solutions of nonlinear Chafee-Infante reaction diffusion equations are constructed.The solutions are of 27 forms.This method used in this paper is widely applicatable for handling other nonlinear reaction diffusion equations.