Soliton gas in integrable dispersive hydrodynamics

Gennady A. El*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)


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.
Original languageEnglish
Article number114001
Pages (from-to)1-69
Number of pages69
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number11
Publication statusPublished - 2 Nov 2021


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