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)]

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

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 >

Language :

Anglais

Popular science :

Non

ANR Project :

Ondes déterministes et aléatoires
Centre Européen pour les Mathématiques, la Physique et leurs Interactions
PSI

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL