Exact wavefronts and periodic patterns in a competition system with nonlinear diffusion

Abstract

We consider a two-species competition system with nonlinear diffusionand exhibit exact solutions of the system.We first show the existence of spatially stationary solutions that are periodic patterns. In a particular case, we also provide a time-dependent solution that approximates this periodic solution.We also show that the system may sustain unbounded wavefronts above the coexistence equilibrium.In the case of equal intrinsic growth rates, we givea sharp wavefront solution with semi-finite support.