Monotone Traveling Wave Solution for a Delayed Reaction-Diffusion Equations

In the paper, we derive a delayed reaction-diffusion equations, which describes a multi-species Predator-prey system. By coupling the perturbation approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist and appear monotone, which connect the zero solution with the positive steady state. Finally, we draw a conclusion to point out that the existence of traveling wave fronts for delayed reaction-diffusion equations is an interesting but difficult problem.