Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation

Thibault Congy*, Gennady El, Giacomo Roberti, Alexander Tovbis

*Corresponding author for this work

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Abstract

We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special ``condensate'' limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the $N$-phase KdV-Whitham modulation equations derived by Flaschka, Forest and McLaughlin (1980) and Lax and Levermore (1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for "diluted'' soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence.
Original languageEnglish
Article number104
Number of pages45
JournalJournal of Nonlinear Science
Volume33
Issue number6
DOIs
Publication statusPublished - 19 Sept 2023

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