Traveling Wave Solutions for a Continuous and Discrete Diffusive Modified Leslie–Gower Predator–Prey Model

In this work, the traveling wave solutions for a modified Leslie-Gower predator–prey model under continuous and discrete diffusion cases are investigated respectively. First, the existence of weak traveling wave solutions is shown by Schauder’s fixed point theorem with the help of positive upper and lower solutions, which can remove the singularity of the system with \(b=0\) $b=0$ at \(u=0\) $u=0$ . Then we use two methods, a squeeze method and a Lyapunov function method, to prove that, under additional conditions, the weak traveling wave solutions are actually traveling wave solutions. Finally, by showing the nonexistence of traveling wave solutions, the minimal wave speed is obtained.