Fronts and pulses in a class of reaction-diffusion equations: a geometric singular perturbations approach

Abstract

In this paper we prove existence of multiplefront solutions in a class of coupled reactiondiusion equations with a small parameter By a travelling wave Ansatz we reduce the problem to a fourdimensional system of ordinary dierential equations and prove existence of a large variety of njump homoclinic and heteroclinic solutions n using geometric singular perturbation theory and Poincare maps Numerical simulations of the reactiondiusion equations indicate that several of the multifront type waves can be stable