Dispersion management in optical fiber links: Integrability in leading nonlinear order

TL;DR

This paper demonstrates that a specific integro-differential equation modeling pulse propagation in dispersion-managed optical fibers is integrable at the leading nonlinear order, with a transformation to the nonlinear Schrödinger equation under weak dispersion conditions.

Contribution

It shows the integrability of the pulse propagation model at leading order and derives the nonintegrable correction, advancing understanding of nonlinear optical fiber dynamics.

Findings

The integro-differential equation is integrable at leading nonlinear order.

A near-identity transformation relates it to the nonlinear Schrödinger equation.

The next order correction is nonintegrable.

Abstract

We show that an integro-differential equation model for pulse propagation in optical transmission lines with dispersion management, is integrable at the {\it leading nonlinear order}. This equation can be transformed into the nonlinear Schroedinger equation by a near-identity canonical transformation for the case of weak dispersion. We also derive the next order (nonintegrable) correction.