Thesis of Loïc Fache

Defense of thesis Loïc Fache - laboratoire PhLAM

Abstract : 

Solitons are stable, localized nonlinear wave packets that emerge in integrable systems from a balance between nonlinearity and dispersion. When large ensembles of solitons interact in random configurations, they form what is known as a soliton gas, a many-body nonlinear wave system whose dynamics call for a statistical treatment. While the theoretical framework for soliton gases has been extensively developed under the assumption of integrability, many physical systems exhibit weak perturbations that break this condition. The impact of such deviations on the spectral and statistical properties of soliton gases remains poorly understood. In this thesis, we experimentally investigate the dynamics of dense soliton gases in three distinct physical platforms: a large deep-water wave tank governed by the focusing nonlinear Schrödinger equation, a nonlinear electrical transmission line modeled by a dissipative KdV equation, and a recirculating optical fiber loop described by a perturbed focusing NLSE. Each system provides a setting to explore the effect of weak integrability breaking, such as damping, diffusion, or optical gain. Our results highlight the limitations of existing kinetic or hydrodynamic theories in weakly non-integrable regimes and point to the need for new frameworks capable of capturing soliton-radiation coupling, spectral reshaping, and non-isospectral evolution.

Keywords : Soliton Gas, Integrable Turbulence, Integrability Breaking, Optics, Inverse Scattering Transform