Fronts and Pulses in a Class of Reaction-diiusion Equations: a Geometric Singular Perturbations Approach

In this paper we prove existence of multiple-front solutions in a class of coupled reaction-diiusion equations with a small parameter. By a travelling wave Ansatz we reduce the problem to a four-dimensional system of ordinary diierential equations and prove existence of a large variety of n-jump homoclinic and heteroclinic solutions, n = 1; 2; 3; : : : using geometric singular perturbation theory and Poincar e maps. Numerical simulations of the reaction-diiusion equations indicate that several of the multi-front type waves can be stable.