Construction of minimizing travelling waves ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Construction of 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]
Smets, Didier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Gravejat, Philippe [Auteur]
Smets, Didier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Journal title :
Tunisian Journal of Mathematics
Pages :
157-188
Publisher :
Mathematical Science Publishers
Publication date :
2024
ISSN :
2576-7658
English keyword(s) :
Defocusing Schrödinger equation
Gross-Pitaevskii equation
travelling waves
planar dark solitons
nonzero conditions at infinity
concentration-compactness
Gross-Pitaevskii equation
travelling waves
planar dark solitons
nonzero conditions at infinity
concentration-compactness
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
As a sequel to our previous analysis in [9] on the Gross-Pitaevskii equation on the product space $\mathbb{R} \times \mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau ...
Show more >As a sequel to our previous analysis in [9] on the Gross-Pitaevskii equation on the product space $\mathbb{R} \times \mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau energy at fixed momentum. We deduce that minimizers are precisely the planar dark solitons when the length of the transverse direction is less than a critical value, and that they are genuinely two-dimensional solutions otherwise. The proof of the existence of minimizers is based on the compactness of minimizing sequences, relying on a new symmetrization argument that is well-suited to the periodic setting.Show less >
Show more >As a sequel to our previous analysis in [9] on the Gross-Pitaevskii equation on the product space $\mathbb{R} \times \mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau energy at fixed momentum. We deduce that minimizers are precisely the planar dark solitons when the length of the transverse direction is less than a critical value, and that they are genuinely two-dimensional solutions otherwise. The proof of the existence of minimizers is based on the compactness of minimizing sequences, relying on a new symmetrization argument that is well-suited to the periodic setting.Show less >
Language :
Anglais
Popular science :
Non
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