Existence of pulses for a monotone reaction-diffusion system

International audienceWe consider a monotone reaction-diffusion system of the form w 1 − w1 + f1(w2) = 0, w 2 − w2 + f2(w1) = 0, and address the question of the existence of pulses, that is of positive decaying at infinity solutions. We prove that pulses exist if and only if the wave speed of the associated travelling-wave problem is positive. The proofs are based on the Leray-Schauder method which uses topological degree for elliptic problems in unbounded domains and a priori estimates of solutions in weighted spaces