Chafee-Infante方程的孤子解

Soliton solution for Chafee-Infante equation

Chafee-Infante方程是一类解决反应扩散问题的重要方程在物理学、化学、生物学、经济学及各种工程问题中有广泛的应用.运用齐次平衡法讨论此方程的孤子解.首先由相容性的条件ωxt=ωtx,求出其特征方程为:2r3+3b(2λ)21r2+(3λb2-λ)r=0,然后依据参数b=0,λ>0及b=1,λ>0的不同情况来讨论其两种情形下解的结构,进而给出它的孤子解.

Chafee-Infante equation is an important class of equations dealing with reaction diffusion problems.It can be applied to many fields,such as physics chemistry biology economics and various engineering problems.This paper uses the homogeneous balance method to discuss the equations for the soliton solution.Firstly by using the compatibility conditions ωxt=ωtx,we find out the characteristic equation：2r3＋3b（2λ）1/2r2＋（3λb2-λ）r=0.Then,based on the parameters of the different situation,we discuss the structures of solution for two cases,and give its soliton solution.