Characterizing far from equilibrium states of the one-dimensional nonlinear Schr{\"o}dinger equation

TL;DR

This paper introduces a new method using inverse scattering transform to identify solitons in far-from-equilibrium 1D nonlinear Schrödinger systems, enabling analysis of soliton distributions in simulations and experiments.

Contribution

It presents a simple, efficient method to identify discrete eigenvalues in the Lax spectrum for the defocusing nonlinear Schrödinger equation, applicable to physical systems.

Findings

Effective identification of solitons in numerical simulations

Benchmark demonstrating method's efficiency

Potential application to experimental data

Abstract

We use the mathematical toolbox of the inverse scattering transform to study quantitatively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schr{\"o}dinger equation. We present a simple method to identify the discrete eigenvalues in the Lax spectrum and provide a extensive benchmark of its efficiency. Our method can be applied in principle to all physical systems described by the defocusing nonlinear Schr{\"o}dinger equation and allows to identify the solitons velocity distribution in numerical simulations and possibly experiments.