Convex compact sets in R^N−1 give traveling fronts of cooperation–diffusion systems in R^N

This paper studies traveling fronts to cooperation–diffusion systems in R^N for N≥3. We consider (N−2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in R^N−1, and define an equivalence relation between them. We prove that there exists a traveling front associated with a given surface and show its stability. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.