Periodic travelling waves on damped 2D lattices with oscillating external forces *

Abstract

Abstract This paper is devoted to periodic travelling waves in a two-dimensional nonautonomous weakly damped lattice system with linear coupling between nearest particles and periodic nonlinear substrate potentials. Nonlinear functional analysis is employed to prove the existence and uniqueness of periodic travelling wave solutions. In the case of small forcing and damping, Lyapunov–Schmidt reduction is employed to study the bifurcation of periodic travelling wave solutions and the asymptotic expressions of the bifurcating solutions.