Existence of traveling wave solutions in a diffusive predator-prey model

We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R-4 and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R-4. The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.