Heredero, Multiscale analysis of discrete nonlinear evolution equations: the reduction of the dNLS

This article is part of the special issue published in honour of Francesco Calogero on the occasion of his 70th birthday In this paper we consider multiple lattices and functions defined on them. We in-troduce some slow varying conditions and define a multiscale analysis on the lattice, i.e. a way to express the variation of a function in one lattice in terms of an asymp-totic expansion with respect to the other. We apply these results to the case of the multiscale expansion of the differential-difference Nonlinear Schrödinger equation.