Generalized hydrodynamics of the attractive non-linear Schrodinger equation

We study the generalized hydrodynamics of the one-dimensional classical non linear Schrodinger 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.

Automated summary

By studying the generalized hydrodynamics of the one-dimensional classical non-linear Schrodinger equation in the attractive phase, we find that the thermodynamic limit is entirely controlled 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 plays a key role as a regulator of the classical soliton gas. We use our results to investigate adiabatic interaction changes from the repulsive to the attractive phase, observing soliton production and obtaining exact analytical results that align excellently with Monte Carlo simulations.