On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type

Onorato, Miguel, Proment, Davide ORCID: https://orcid.org/0000-0002-9472-0097, El, Gennady, Randoux, Stephane and Suret, Pierre (2016) On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type. Physics Letters A, 380 (39). pp. 3173-3177. ISSN 0375-9601

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We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results.

Item Type: Article
Uncontrolled Keywords: rogue waves,freak waves,nonlinear schrödinger
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Quantum Fluids
Faculty of Science > Research Groups > Centre for Photonics and Quantum Science
Depositing User: Pure Connector
Date Deposited: 24 Sep 2016 00:11
Last Modified: 09 Feb 2023 13:43
URI: https://ueaeprints.uea.ac.uk/id/eprint/59901
DOI: 10.1016/j.physleta.2016.07.048


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