Soliton gas in integrable dispersive hydrodynamics

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

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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
Uncontrolled Keywords: Soliton Gas, Dispersive Hydrodynamics, Spectral Kinetic 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: 30 Sep 2021 16:45
URI: http://nrl.northumbria.ac.uk/id/eprint/46877

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