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On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type
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 th...
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| Main Authors: | , , , , |
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| Format: | Default Article |
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2016
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| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/22194 |
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| _version_ | 1818171849937256448 |
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| author | Miguel Onorato Davide Proment Gennady El Stephane Randoux Pierre Suret |
| author_facet | Miguel Onorato Davide Proment Gennady El Stephane Randoux Pierre Suret |
| author_sort | Miguel Onorato (279705) |
| collection | Figshare |
| description | 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. |
| format | Default Article |
| id | rr-article-9385484 |
| institution | Loughborough University |
| publishDate | 2016 |
| record_format | Figshare |
| spelling | rr-article-93854842016-07-26T00:00:00Z On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type Miguel Onorato (279705) Davide Proment (279706) Gennady El (1258536) Stephane Randoux (7159871) Pierre Suret (7159868) Other mathematical sciences not elsewhere classified Rogue waves Freak waves Nonlinear Schrodinger Mathematical Sciences not elsewhere classified 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. 2016-07-26T00:00:00Z Text Journal contribution 2134/22194 https://figshare.com/articles/journal_contribution/On_the_origin_of_heavy-tail_statistics_in_equations_of_the_Nonlinear_Schrodinger_type/9385484 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified Rogue waves Freak waves Nonlinear Schrodinger Mathematical Sciences not elsewhere classified Miguel Onorato Davide Proment Gennady El Stephane Randoux Pierre Suret On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title | On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title_full | On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title_fullStr | On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title_full_unstemmed | On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title_short | On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type |
| title_sort | on the origin of heavy-tail statistics in equations of the nonlinear schrodinger type |
| topic | Other mathematical sciences not elsewhere classified Rogue waves Freak waves Nonlinear Schrodinger Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/22194 |