Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves

TL;DR

This paper demonstrates the first controlled experimental synthesis of a dense soliton gas in deep-water waves using nonlinear spectral theory, revealing how higher-order effects influence the soliton ensemble.

Contribution

It provides the first experimental realization of a soliton gas in water and applies nonlinear spectral analysis to understand its dynamics and perturbative effects.

Findings

Successful synthesis of a dense soliton gas in a water tank.

Control and measurement of the spectral density of states.

Observation of slow changes in the density due to higher-order effects.

Abstract

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. Despite significant theoretical developments and observational evidence of ubiquity of soliton gases in fluids and optical media their controlled experimental realization has been missing. We report the first controlled synthesis of a dense soliton gas in deep-water surface gravity waves using the tools of nonlinear spectral theory (inverse scattering transform (IST)) for the one-dional focusing nonlinear Schr\"odinger equation. The soliton gas is experimentally generated in a one-dimensional water tank where we demonstrate that we can control and measure the density of states, i. e. the probability density function parametrizing the soliton gas in the IST spectral phase space. Nonlinear spectral analysis of the generated hydrodynamic soliton gas reveals that the density of states slowly changes under the influence of perturbative higher-order effects that break the integrability of the wave dynamics.