Existence and multiplicity of traveling waves in a lattice dynamical system

Abstract

This work proves the existence and multiplicity results of monotonic traveling wave solutions for some lattice differential equations by using the monotone iteration method. Our results include the model of cellular neural networks (CNN). In addition to the monotonic traveling wave solutions, non-monotonic and oscillating traveling wave solutions in the delay type of CNN are also obtained. (C) 2000 Academic Press.