Vendredi 27 juin 2025
Salle de conférences IRMA
This is a colloquium in Physics and Mathematics, organised biannually in Strasbourg by a group of scientists from IRMA, ISIS and IPCMS.
This seventh session is devoted to Soliton gases.
Organizers : N. Anantharaman, R. Côte, V. Dang, S. Klevtsov, Y. Le Floch, M. Vogel, X. Zeng (IRMA) — J. Dubail, D. Hagenmuller, S. Whitlock (CESQ) — G. Pupillo, J. Schachenmayer (ISIS) — P.-A. Hervieux, R. Jalabert, G. Manfredi, G. Weick, D. Weinmann (IPCMS)
Speakers :
- Benjamin Doyon (King's College London)
- Pierre Suret (Lille)
Location : Salle de conférences IRMA
For practical and other questions please contact the organizers.
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Vendredi 27 juin 2025
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09:30
Pierre Suret, University of Lille
Integrable turbulence, soliton gas and Generalized Gibbs ensembles
The concept of a soliton gas was first introduced by V. Zakharov in 1971 as an infinite ensemble of weakly interacting solitons within the framework of the Korteweg–de Vries (KdV) equation [1]. In this theoretical model of a rarefied soliton gas, solitons with randomly distributed amplitudes and phases interact minimally and remain mostly non- overlapping. More recently, this concept has been extended to dense soliton gases, where strong and continuous interactions occur between solitons. Soliton gases are inherently linked to integrable wave systems described by nonlinear partial differential equations, such as the KdV equation or the one-dimensional nonlinear Schr¨odinger equation, which can be solved using the inverse scattering transform. Over the past few years, the study of soliton gases has gained significant traction in both theoretical and experimental research. In particular, it has been recognized that soliton gas dynam- ics play a crucial role in fundamental nonlinear wave phenomena, including spontaneous modulation instability [2]. Moreover, recent discoveries have revealed profound connections between soliton gas theory and generalized hydrodynamics [3], expanding the scope of the field and raising new fundamental questions related to soliton gas thermodynamics and statistical properties. In this talk, we will review the latest theoretical and experimental advancements in the study of soliton gases. We will introduce key conceptual tools, such as the inverse scattering transform, and the Generalized Gibbs Ensemble. [1] VE Zakharov: Kinetic equation for solitons, Sov. Phys. JETP 33, 538–540 (1971) [2] Adrien E. Kraych, Dmitry Agafontsev, Stephane Randoux, and Pierre Suret: Statistical properties of the nonlinear stage of modulation instability in fiber optics Phys. Rev. Lett. 123, 093902 (2019). [3] P Suret, S Randoux, A Gelash, D Agafontsev, B Doyon, G El: Soliton gas: Theory, numerics, and experiments Phys. Rev. E 109 (6), 061001 (2024) -
10:30
Pause Café
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11:00
Benjamin Doyon, King's College, London
The hydrodynamic of integrable systems: from soliton gas to quantum gas
Hydrodynamic theory is a powerful framework to describe observations at large scales of space and time in systems subject to microscopic fluctuations. It is usually applied to chaotic systems, where one gets equations for the transport of energy, momentum and particle. But it turns out that chaos is not necessary: integrable systems also have a well defined hydrodynamic scale. This is the theory of generalised hydrodynamics. It is based on the idea of local relaxation to generalised Gibbs ensembles, and accounts for the infinite number of conserved quantities. I will introduce the main hydrodynamic concepts behind this theory and show how it applies to a wide variety of systems, from the simple model of hard spheres in one dimension, to soliton gases (Pierre’s talk) and quantum gases. I will also review some of the recent advances, as time permits, such as correlations, fluctuations, and the diffusive scale and beyond. -
12:00
Lunch At "le 32"