On the Integrability of the Discrete Nonlinear Schroedinger Equation

TL;DR

This paper provides analytical evidence that the discrete nonlinear Schrödinger equation is not integrable, using a reductive perturbation technique to identify obstructions to integrability.

Contribution

It offers the first analytic proof of the non-integrability of the discrete nonlinear Schrödinger equation, clarifying its mathematical properties.

Findings

Evidence of non-integrability through reductive perturbation analysis

Identification of obstructions to integrability in the equation

Clarification of the equation's mathematical structure

Abstract

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.