Multiscale reduction of discrete nonlinear Schroedinger equations

TL;DR

This paper employs discrete multiscale analysis to investigate the asymptotic integrability of differential-difference equations, specifically applying it to two discretizations of the nonlinear Schrödinger equation to derive integrability conditions.

Contribution

It introduces a multiscale perturbation approach as an analytic method to assess integrability of discretized nonlinear Schrödinger equations.

Findings

Multiscale analysis identifies integrability conditions for discretizations.

Provides a systematic way to analyze asymptotic integrability.

Applies method to well-known discretizations of NLS.

Abstract

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.