Uniqueness of Traveling Waves for a Two-Dimensional Bistable Periodic Lattice Dynamical System

Abstract

We study traveling waves for a two-dimensional lattice dynamical system with bistable nonlinearity in periodic media. The existence and the monotonicity in time of traveling waves can be derived in the same way as the one-dimensional lattice case. In this paper, we derive the uniqueness of nonzero speed traveling waves by using the comparison principle and the sliding method.