Traveling waves of some Holling-Tanner predator-prey system with nonlocal diffusion

This paper is devoted to establish the existence and non-existence of the traveling waves for the nonlocal Holling-Tanner predator-prey model. By applying the Schauder's fixed point theorem, we can obtain the existence of the traveling waves. Moreover, in order to prove the limit behavior of the traveling waves at infinity, we construct a sequence that converges to the coexistence state. For the proof of the nonexistence of the traveling waves, we use the property of the two-sided Laplace transform. Finally, we give the effect of the nonlocal diffusion term for the traveling waves.