Explicit breather solution of the nonlinear Schr\"odinger equation

TL;DR

This paper derives a simple closed-form expression for a three-parameter breather solution of the nonlinear Schrödinger equation, facilitating experimental verification and analysis of pulse dynamics in optical fibers.

Contribution

It provides the first explicit analytic formula for the three-parameter breather, enabling easier experimental validation and deeper understanding of nonlinear pulse behavior.

Findings

Analytic proof of time period doubling in breathers

Simplified experimental verification of breather pulses

Explicit three-parameter breather formula

Abstract

We present a one-line closed form expression for the three-parameter breather of the nonlinear Schr\"odinger equation. This provides an analytic proof of the time period doubling observed in experiments. The experimental check that some pulses generated in optical fibers are indeed such generalized breathers will be drastically simplified.