FACHE Loïc : Optical and Hydrodynamical soliton gases

Résumé de thèse :

This presentation offers a synthesis of two experimental studies focusing on the Soliton gas propagation.

The first investigation examines the experimental demonstration of Korteweg-de Vries (KdV) dynamics at the leading order in a discrete nonlinear electrical transmission line composed of LC oscillators with voltage- dependent capacitance [1]. By using the Inverse Scattering Transform (IST) formalism, the propagation of waves within this system, governed by the KdV-Burgers equation (KdV with a small diffusion term), is explored. Through the generation and implementation of a soliton gas using numerical methods [2], the spatiotemporal dynamics and density of state evolution are observed.

The second study [3] focuses on hydrodynamic experiments exploring the interaction (collision) between two sets of soliton gases, referred to as monochromatic soliton gases with identical amplitudes but opposite velocities [4]. By varying their relative initial velocities, changes in the interaction force between the two gases are investigated. The spatiotemporal evolution and induced velocity changes are recorded in a 140-meter-long water tank, revealing quantitative agreement with predictions from the kinetic theory of soliton gases. Moreover, the robustness of these findings to perturbative nonlinear effects, breaking the integrability of wave dynamics, is observed.

[1] D. S. Ricketts & D. Ham, Electrical solitons: theory, design, and applications, CRC Press (2018)
[2] G-J. Liao & N-N. Huang, Method of Darboux Transformation Matrix for the KdV Equation, Commun. Theor. Phys., 25, 183-188 (1996).
[3] Fache Loïc, Bonnefoy Félicien, Ducrozet Guillaume, Copie François, Novkoski Filip, Ricard Guillaume, Roberti Giacomo, Falcon Eric, Suret Pierre, El Gennady, Randoux Stéphane, Phys. Rev. E (2024).
[4] El G. A., Kamchatnov A. M., Phys. Rev. Lett. (2005).

Doctorant : FACHE Loïc

Directeur de thèse : RANDOUX Stéphane