@article{1a50fc27909441d7aebea1f88f4c009a,

title = "Statistics of extreme events in integrable turbulence",

abstract = "We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr¨odinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous (noise induced) modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular non-bound state gas is considered providing important insights related to the validity of the so-called virial theorem.",

author = "T. Congy and El, {G. A.} and G. Roberti and A. Tovbis and S. Randoux and P. Suret",

note = "Funding Information: This work has been partially supported by the Agence Nationale de la Recherche through the LABEX CEMPI project (ANR-11-LABX-0007) and the SOGOOD project (ANR-21-CE30-0061), the Ministry of Higher Education and Research, Hauts de France council, the European Regional Development Fund (ERDF) through the Nord-Pas de Calais Regional Research Council and the European Regional Development Fund (ERDF) through the Contrat de Projets Eta-R´egion (CPER Photonics for Society P4S). The authors would like to thank the Isaac Newton Institute (INI) for Mathematical Sciences for support and hospitality during the programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves” when part of the work on this paper was undertaken. The work of AT, TC and GR was partially supported by the Simons Fellowships during the INI Programme. GE{\textquoteright}s and GR{\textquoteright}s work was also partially supported by EPSRC Grant Number EP/W032759/1. A.T. was supported in part by the National science Foundation grant DMS-2009647.",

year = "2023",

month = dec,

day = "21",

language = "English",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

}