Existence and uniqueness of traveling waves for a monostable 2-D lattice dynamical system

Abstract

We study traveling waves for a two-dimensional lattice dynamical system with monostable nonlinearity. We prove that there is a minimal speed such that a traveling wave exists if and only if its speed is above this minimal speed. Then we show the uniqueness (up to translations) of wave profile for each given speed. Moreover, any wave profile is strictly monotone.