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

Miguel Onorato, Davide Proment, Gennady El, Stéphane Randoux, Pierre Suret

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)
5 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)3173-3177
JournalPhysics Letters A
Volume380
Issue number39
Early online date26 Jul 2016
DOIs
Publication statusPublished - 16 Sep 2016

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