On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2017

On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation

Résumé

We consider the one-dimensional Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we show the persistence of the stationary black soliton of the unperturbed problem as a solution. We also prove the existence of another branch of non-trivial stationary waves. Depending on the attractive or repulsive nature of the Dirac perturbation and of the type of stationary solutions, we prove orbital stability via a variational approach, or linear instability via a bifurcation argument.
Fichier principal
Vignette du fichier
ianni-lecoz-royer-2016-09-02.pdf (645.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01163000 , version 1 (11-06-2015)
hal-01163000 , version 2 (13-06-2016)
hal-01163000 , version 3 (14-12-2016)

Identifiants

Citer

Isabella Ianni, Stefan Le Coz, Julien Royer. On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation. SIAM Journal on Mathematical Analysis, 2017, 49 (2), pp.1060-1099. ⟨10.1137/15M1029606⟩. ⟨hal-01163000v3⟩
401 Consultations
166 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More