Multiple branches of travelling waves for the Gross Pitaevskii equation

Abstract : Explicit solitary waves are known to exist for the Kadomtsev-Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross-Pitaevskii (GP) equation which in some long wave regime converges to the (KP-I) equation. Numerical simulations already showed that a branch of travelling waves of (GP) converges to a ground state of (KP-I), expected to be the lump. In this work, we perform numerical simulations showing that the other explicit solitary waves solutions to the (KP-I) equation give rise to new branches of travelling waves of (GP) corresponding to excited states.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01525255
Contributeur : David Chiron <>
Soumis le : vendredi 19 mai 2017 - 16:49:03
Dernière modification le : jeudi 15 juin 2017 - 09:09:33

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  • HAL Id : hal-01525255, version 1

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David Chiron, Claire Scheid. Multiple branches of travelling waves for the Gross Pitaevskii equation. 2017. <hal-01525255>

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