Bound-state soliton gas as a limit of adiabatically growing integrable turbulence

TL;DR

This study numerically investigates integrable turbulence in the 1D-NLSE, revealing a universal adiabatic growth regime leading to a dense bound-state soliton gas, with soliton properties influenced by initial noise spectrum.

Contribution

It introduces a new 'growing of turbulence' approach and demonstrates the universal adiabatic regime and soliton gas formation in integrable turbulence.

Findings

Universal adiabatic growth regime observed

Soliton gas properties depend on initial noise spectrum

Transition from weakly to strongly nonlinear states with rogue waves

Abstract

We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the "growing of turbulence". In this approach, we add a small linear pumping term to the equation and start evolution from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and examine the resulting integrable turbulence. For sufficiently small initial noise and pumping coefficient, and also for not very wide simulation box (basin length), we observe that the turbulence grows in a universal adiabatic regime, moving successively through the statistically stationary states of the integrable 1D-NLSE, which do not depend on the pumping coefficient, amplitude of the initial noise or basing length. Waiting longer in the growth stage, we transit from weakly nonlinear states to strongly nonlinear ones, characterized by a high frequency of rogue waves. Using the inverse scattering transform (IST) method to monitor the evolution, we observe that the solitonic part of the wavefield becomes dominant even when the (linear) dispersion effects are still leading in the dynamics and with increasing average intensity the wavefield approaches a dense bound-state soliton gas, whose properties are defined by the Fourier spectrum of initial noise. Regimes deviating from the universal adiabatic growth also lead to solitonic states, but solitons in these states have noticeably different velocities and a significantly wider distribution by amplitude, while the statistics of wavefield indicates a much more frequent appearance of very large waves.