Minimizing travelling waves for the ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Minimizing travelling waves for the Gross-Pitaevskii equation on $\mathbb{R} \times \mathbb{T}$
Author(s) :
De Laire, André [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Gravejat, Philippe [Auteur]
Analyse, Géométrie et Modélisation [AGM - UMR 8088]
Smets, Didier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
![refId](/themes/Mirage2//images/idref.png)
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Gravejat, Philippe [Auteur]
Analyse, Géométrie et Modélisation [AGM - UMR 8088]
Smets, Didier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Journal title :
Annales de la Faculté des Sciences de Toulouse. Mathématiques.
Publisher :
Université Paul Sabatier _ Cellule Mathdoc
Publication date :
2024
ISSN :
0240-2963
English keyword(s) :
Gross-Pitaevksii equation
Travelling waves
Travelling waves
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space $ \mathbb{R} \times \mathbb{T}_L$ where $L > 0$ and $\mathbb{T}_L = \mathbb{R} / L ...
Show more >We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space $ \mathbb{R} \times \mathbb{T}_L$ where $L > 0$ and $\mathbb{T}_L = \mathbb{R} / L \mathbb{Z}$. We focus on the variational problem consisting in minimizing the Ginzburg-Landau energy under a fixed momentum constraint. We prove that there exists a threshold value for L below which minimizers are the one-dimensional dark solitons, and above which no minimizer can be one-dimensional.Show less >
Show more >We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space $ \mathbb{R} \times \mathbb{T}_L$ where $L > 0$ and $\mathbb{T}_L = \mathbb{R} / L \mathbb{Z}$. We focus on the variational problem consisting in minimizing the Ginzburg-Landau energy under a fixed momentum constraint. We prove that there exists a threshold value for L below which minimizers are the one-dimensional dark solitons, and above which no minimizer can be one-dimensional.Show less >
Language :
Anglais
Popular science :
Non
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