Traveling wave solutions for diffusive predator-prey type systems with nonlinear density dependence

Traveling wave solution for a class of diffusive predator-prey system with nonlinear density dependence is considered. Using methods of topological shooting, we show the existence of a non-negative traveling wave solution connecting a boundary equilibrium to the co-existence steady state with the help of a Wazewski-like set together with Lyapunov function constructed elaborately. This means that the traveling wave solution established by Huang (2012) can be preserved in the presence of the nonlinear density dependence for the predator and the results of Huang (2012) are generalized.