Traveling waves for nonlocal Lotka-Volterra competition systems

In this paper, we study the traveling wave solutions of a Lotka-Volterra diffusion competition system with nonlocal terms. We prove that there exists traveling wave solutions of the system connecting equilibrium $ (0, 0) $ to some unknown positive steady state for wave speed $ c>c^* = \max\left\{2, 2\sqrt{dr}\right\} $ and there is no such traveling wave solutions for $ c