Soliton gas in integrable dispersive hydrodynamics

El, Gennady (2021) Soliton gas in integrable dispersive hydrodynamics. Journal of Statistical Mechanics: Theory and Experiment, 2021 (11). p. 114001. ISSN 1742-5468

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Official URL: https://doi.org/10.1088/1742-5468/ac0f6d

Abstract

We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and the focusing nonlinear Schrödinger equations. For the focusing nonlinear Schrödinger equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. Integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.

Item Type: Article
Additional Information: Funding information: This work was partially supported by EPSRC Grant EP/R00515X/2. I would like to express my gratitude to the late A L Krylov, who had suggested this topic to me many years ago. I am grateful to M Hoefer, A Kamchatnov, M Pavlov, S Randoux, P Suret and A Tovbis for the collaboration and many stimulating discussions over the years. I would like to thank T Congy and G Roberti for their more recent contributions and for the help with preparing the figures. Special thanks to T Bonnemain for reading the manuscript and providing a number of helpful comments.
Uncontrolled Keywords: nonlinear dynamics, classical integrability, non-linear Schroedinger equation
Subjects: F300 Physics
H800 Chemical, Process and Energy Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Rachel Branson
Date Deposited: 09 Aug 2021 10:11
Last Modified: 01 Dec 2021 13:02
URI: http://nrl.northumbria.ac.uk/id/eprint/46877

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