Title :

Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity

Author(s) :

De Laire, André [Auteur]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Mennuni, Pierre [Auteur]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]

Journal title :

Discrete and Continuous Dynamical Systems - Series A

Pages :

635-682

Publisher :

American Institute of Mathematical Sciences

Publication date :

2020-01

ISSN :

1078-0947

English keyword(s) :

orbital stability
dark soli- tons
nonzero conditions at infinity
dark solitons
Nonlocal Schrödinger equation
Gross-Pitaevskii equation
traveling waves

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions ...
Show more >We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions with nonvanishing conditions at infinity. Moreover, we show that the branch is orbitally stable. In this manner, this result generalizes known properties for the contact interaction given by a Dirac delta function. Our proof relies on the minimization of the energy at fixed momentum. As a by-product of our analysis, we provide a simple condition to ensure that the solution to the Cauchy problem is global in time.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL