The study of rogue waves is a booming topic mainly in oceanography but also in other fields. In this thesis I construct via Darboux transform a multi-parametric family of smooth quasi-rational solutions of the nonlinear Schödinger equation that present a behavior of rogue waves. For a general choice of parameters the second-order solutions give a model of "three sisters" (three higher than expected waves in a row) while for a particular choice of parameters we obtain the solutions given by Akhmediev et al. in a serie of articles in 2009. Then these solutions allow me to construct rational solutions of the KP-I equation that describe waves in shallow water.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00625446 |
| Date | 14 December 2010 |
| Creators | Dubard, Philippe |
| Publisher | Université de Bourgogne |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | English |
| Detected Language | English |
| Type | PhD thesis |
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