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 >= c & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c\ge c<^>*$$\end{document} when n >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 0$$\end{document}. In addition, we obtain the minimal wave speed c & lowast;=2r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c<^>*= 2\sqrt{r}$$\end{document} when n=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=0$$\end{document}, 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.