Traveling waves of a modified Holling-Tanner predator–prey model with degenerate diffusive

This paper is concerned with the traveling waves for a modified Holling-Tanner predator–prey model with degenerate diffusion. Different from the established approaches of constructing upper-lower solutions, we construct a new and suitable pair of upper-lower solutions by solving three differential equations and establish the existence of traveling waves for any \(c\ge c^*\) $c\ge c^{\ast }$ when \(n\ge 0\) $n\ge 0$ . In addition, we obtain the minimal wave speed \(c^*= 2\sqrt{r}\) $c^{\ast }=2\sqrt{r}$ when \(n=0\) $n=0$ , without reconstructing the upper-lower solutions. Furthermore, the asymptotic behavior of traveling waves at infinity is obtained by the upper-lower solutions and the contracting rectangle method.