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Ondes progressives pour les équations de Gross-Pitaevskii

Abstract : This PhD thesis is devoted to the travelling waves in the Gross-Pitaevskii equation, and the solitary waves in the generalised Kadomtsev-Petviashvili equations.

The Gross-Pitaevskii equation is a model for Bose-Einstein condensates, superconductivity, superfluidity or non-linearoptics. The generalised Kadomtsev-Petviashvili equations arise in the study of weakly non-linear, dispersive waves, and sound waves in anti-ferromagnetics.

Here, we investigate the existence properties and the asymptotic behaviour of such waves. We first establish the non-existence of non-constant supersonic travelling waves of finite energy in the Gross-Pitaevskii equation in dimension larger than two, and of non-constant sonic travelling waves of finite energy in the Gross-Pitaevskii equation in dimension two. We then describe the asymptotic behaviour of subsonic travelling waves of finite energy in the Gross-Pitaevskii equation, and of solitary waves in the generalised Kadomtsev-Petviashvili equations, in dimension larger than two.
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Submitted on : Saturday, January 26, 2008 - 11:12:21 AM
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Philippe Gravejat. Ondes progressives pour les équations de Gross-Pitaevskii. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00218296⟩

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