The existence and stability of traveling waves with transition layers for the S-K-T competition model with cross-diffusion

This paper is concerned with the existence and stability of traveling waves with transition layers for a quasi-linear competition system with cross diffusion,which was first proposed by Shegesada,Kawasaki and Teramoto.When one of the random diffusion rates is small and the cross-diffusion rate is not small,by the geometric singular perturbation method,the existence of traveling waves with transition layers is obtained.Further,by the detailed spectral analysis and topological index method,the traveling waves...