Traveling waves in time periodic lattice differential equations

Abstract

The current paper concerns with traveling wave solutions to time periodic two-dimensional lattice differential equations of bistable type. Employing the so-called ‘vanishing viscosity’ approach, we obtain the existence of monotone traveling wave solutions connecting the two spatially homogeneous periodic solutions. Uniqueness of the wave speed and uniqueness of continuous wave front are shown by repeatedly utilizing comparison arguments. The existence and uniqueness results of the current paper together with the stability results proved in an author's earlier paper generalize those in the time-independent case.