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Extreme wave solutions: Parametric studies and wavelet analysis |
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| Affiliation: | 1. Doctoral School in Theoretical and Applied Mechanics, Università di Roma La Sapienza, 18 Via Eudossiana, Rome;2. MeMoCS, International Research Center for the Mathematics & Mechanics of Complex Systems, Università dell׳Aquila, Italy;3. Department of Structural and Geotechnical Engineering, Università di Roma La Sapienza, 18 Via Eudossiana, Rome;4. Department of Physics, University Federico II, Naples, Via Cinthia I-80126, Naples, Italy;1. Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, bldg 1, 119526 Moscow, Russia;2. Bauman Moscow State Technical University, 5 Second Baumanskaya Street, 105005 Moscow, Russia;3. National Research Nuclear University MEPhI, 31 Kashirskoe Shosse, 115409 Moscow, Russia;4. Cardiff University, Heath Park, Cardiff CF14 4XY, UK |
| Abstract: | Wave fields for near homoclinic, single mode rogue-wave solutions of the periodic nonlinear Schrödinger equation are presented. Parameters of candidate solutions are estimated and refined through an eigenvalue solution procedure. An overview of the estimation and refining procedure used by the authors is provided. Solutions are scaled to facilitate experimental implementation. The continuous wavelet transform is used to carry out time–frequency analyses and the results obtained are demonstrative of the dispersion relation as well as the time varying side band energy transfer associated with the Benjamin–Feir instability. The analysis framework and approach used are validated with the Peregrine solution. Other extreme wave solutions are analyzed as well. The framework presented here could serve as a basis for experimental investigations into single mode rogue waves as well as other localizations in wave fields. |
| Keywords: | Nonlinear Schrödinger equation Rogue waves Graphics processing unit based computations Time–frequency analyses |
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