Multi-rogue solutions to the focusing NLS equation

Abstract : 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.
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Philippe Dubard. Multi-rogue solutions to the focusing NLS equation. General Mathematics [math.GM]. Université de Bourgogne, 2010. English. ⟨NNT : 2010DIJOS050⟩. ⟨tel-00625446⟩

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