Qualitative Analysis and Travelling Wave Solutions for the Chaffee–Infante Equation

Abstract

This paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions to the Chaffee–Infante equation. By qualitative analysis, global phase portraits of the dynamic system corresponding to the equation are obtained for different parameter conditions. Furthermore, the relations between the properties of travelling wave solutions and the diffusion coefficient λ of the equation are investigated. In addition, all possible kink profile solitary wave solutions and approximate damped oscillatory solutions to the equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. Based on these studies, the main contribution in this paper is to reveal the diffusion effect on travelling wave solutions to the Chaffee–Infante equation.