@article{cdaf0b0ee39448deaa36ac48ac0b1e92,
title = "Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation",
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.",
author = "Thibault Congy and Gennady El and Giacomo Roberti and Alexander Tovbis",
note = "Funding information: The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves” when the work on this paper was undertaken. This work was supported by EPSRC Grant Number EP/R014604/1. GE{\textquoteright}s and GR{\textquoteright}s work was also supported by EPSRC Grant Number EP/W032759/1 and AT{\textquoteright}s work was supported by NSF Grant DMS 2009647. TC, GR and AT thank Simons Foundation for partial support. All authors thank T. Bonnemain, S. Randoux and P. Suret for numerous useful discussions.",
year = "2023",
month = sep,
day = "19",
doi = "10.1007/s00332-023-09940-y",
language = "English",
volume = "33",
journal = "Journal of Nonlinear Science",
issn = "0938-8974",
publisher = "Springer",
number = "6",
}