Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation

TL;DR

This paper develops a generalized hydrodynamics framework for the one-dimensional attractive Non-Linear Schroedinger equation, revealing solitonic modes dominate the thermodynamics and providing analytical insights into soliton production during phase transitions.

Contribution

It introduces a novel hydrodynamic approach for the attractive phase, connecting semiclassical quantum Bose gas limits with classical soliton dynamics.

Findings

Thermodynamics is dominated by solitonic modes with no radiation.

Exact analytical results match Monte Carlo simulations during phase transitions.

Soliton production is characterized during adiabatic interaction changes.

Abstract

We study the generalized hydrodynamics of the one-dimensional classical Non Linear Schroedinger equation in the attractive phase. We thereby show that the thermodynamic limit is entirely captured by solitonic modes and radiation is absent. Our results are derived by considering the semiclassical limit of the quantum Bose gas, where the Planck constant has a key role as a regulator of the classical soliton gas. We use our result to study adiabatic interaction changes from the repulsive to the attractive phase, observing soliton production and obtaining exact analytical results which are in excellent agreement with Monte Carlo simulations.