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

Onorato, Miguel, Proment, Davide, 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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Official URL: https://doi.org/10.1016/j.physleta.2016.07.048

Abstract

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
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 03 Dec 2018 13:20
Last Modified: 24 Apr 2019 09:00
URI: http://nrl.northumbria.ac.uk/id/eprint/37041

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