Exponential decay of dispersion managed solitons for vanishing average dispersion

TL;DR

This paper proves that dispersion managed solitons decay exponentially in space and frequency, confirming a longstanding conjecture and advancing understanding of their behavior in optical fiber systems.

Contribution

It establishes the exponential decay of solutions to the Gabitov-Turitsyn equation, confirming Lushnikov's conjecture about dispersion managed solitons.

Findings

Solutions decay exponentially in space and frequency domains.

Confirms Lushnikov's conjecture on exponential decay.

Provides mathematical proof for decay properties of solitons.

Abstract

We show that any $L^2$ solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the affirmative Lushnikov's conjecture of exponential decay of dispersion managed solitons.