Travelling Waves for Reaction Diffusion Equations

Abstract

In this paper the travelling waves for the reaction diffusion equation in most general case is considered. The existence of travelling wave solutions is proved under very weak conditions, which are also necessary for the nonlinear term. A difference method is suggested and Leray-Scbauder fixed point theorem is used to prove the existence of discrete travelling waves. Then the convergence is shown and so the solution for the differential equation is obtained.