The global structure of traveling waves in spatially discrete dynamical systems

We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely, lattice differential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c ≠ 0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c ≠ 0. Convergence results for solutions are obtained at the singular perturbation limit c → 0. © 1999 Plenum Publishing Corporation.