Exponential Decay for dispersion managed solitons for general dispersion profiles

TL;DR

This paper proves that dispersion managed solitons and their Fourier transforms decay exponentially under general dispersion profiles, extending previous results to broader physical scenarios.

Contribution

It establishes exponential decay for solutions of the Gabitov-Turitsyn equation with general dispersion profiles, broadening the applicability of prior decay results.

Findings

Solutions and their Fourier transforms decay exponentially.

Applicable to arbitrary non-negative average dispersion.

Covers most physically relevant dispersion profiles.

Abstract

We show that any weak solution of the Gabitov-Turitsyn equation describing dispersion managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdogan, Hundertmark and Lee in two directions, to arbitrary non-negative average dispersion and, more importantly, to rather general dispersion profiles, which cover most, if not all, physically relevant cases.