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

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• 作者：Miguel Onorato^a ; ^b ; ^{miguel.onorato@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Davide Proment^c ; Gennady El^d ; Stephane Randoux^e ; Pierre Suret^e
• 关键词：Rogue waves ; Freak waves ; Nonlinear Schrö ; dinger
• 刊名：Physics Letters A
• 出版年：2016
• 出版时间：16 September 2016
• 年：2016
• 卷：380
• 期：39
• 页码：3173-3177
• 全文大小：837 K

文摘

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.