Nonlinear Spectral Synthesis of Soliton Gas

in Deep-Water Surface Gravity Waves

¹Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molecules, F-59 000 Lille, France

²Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
³Institute of Automation and Electrometry SB RAS, Novosibirsk 630090, Russia
⁴Skolkovo Institute of Science and Technology, Moscow 121205, Russia
⁵Ecole Normale Supérieure, LP, PSL*, UMR 8550 CNRS, F-75 205 Paris, France

⁶Sorbonne Université, IJLRA, UMR 7190 CNRS, F-75 005 Paris, France
⁷Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
⁸Math. Dpt, Physics and Electrical Eng., Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom

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 Schrödinger 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.

Press items:

"Controlled generation of a soliton gas", MSC Laboratory Web Site, March 19, 2021 (in french)
"First controlled generation of a dense soliton gas" in Actualités Scientifiques du CNRS, Feb. 15, 2021 (in french), (or see in PDF)
and in CNRS Hebdo Feb. 18, 2021, and in Tweeter_@INSIS_CNRS Feb. 17, 2021