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

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

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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.
Original languageEnglish
Pages (from-to)3173-3177
Number of pages5
JournalPhysics Letters A
Issue number39
Early online date26 Jul 2016
Publication statusPublished - 16 Sep 2016


  • Rogue waves
  • Freak waves
  • Nonlinear Schrödinger

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