Multiscale Analysis of Discrete Nonlinear Evolution Equations

Abstract

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon chain, the Takeno system and a discrete version of the Benjamin-Bona-Mahoney equation. Among the resulting limit models we find a discrete nonlinear Schroedinger equation (with reversed space-time), a 3-wave resonant interaction system and a discrete modified Volterra model.