Existence and decay of traveling waves for ...
Document type :
Article dans une revue scientifique: Article original
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Title :
Existence and decay of traveling waves for the nonlocal Gross-Pitaevskii equation
Author(s) :
De Laire, André [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Communications in Partial Differential Equations
Pages :
1732-1794
Publisher :
Taylor & Francis
Publication date :
2022
ISSN :
0360-5302
English keyword(s) :
Nonlocal Schrödinger equation
Gross-Pitaevskii equation
traveling waves
dark solitons
nonzero conditions at infinity
decay
analyticity.
Gross-Pitaevskii equation
traveling waves
dark solitons
nonzero conditions at infinity
decay
analyticity.
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
We consider the nonlocal Gross-Pitaevskii equation that models a Bose gas with general nonlocal interactions between particles in one spatial dimension, with constant density far away. We address the problem of the existence ...
Show more >We consider the nonlocal Gross-Pitaevskii equation that models a Bose gas with general nonlocal interactions between particles in one spatial dimension, with constant density far away. We address the problem of the existence of traveling waves with nonvanishing conditions at infinity, i.e. dark solitons. Under general conditions on the interactions, we prove existence of dark solitons for almost every subsonic speed. Moreover, we show existence in the whole subsonic regime for a family of potentials. The proofs are based on a Mountain Pass argument combined with the so-called "monotonicity trick", as well as on a priori estimates for the Palais-Smale sequences. Finally, we establish properties of the solitons such us exponential decay at infinity and analyticity.Show less >
Show more >We consider the nonlocal Gross-Pitaevskii equation that models a Bose gas with general nonlocal interactions between particles in one spatial dimension, with constant density far away. We address the problem of the existence of traveling waves with nonvanishing conditions at infinity, i.e. dark solitons. Under general conditions on the interactions, we prove existence of dark solitons for almost every subsonic speed. Moreover, we show existence in the whole subsonic regime for a family of potentials. The proofs are based on a Mountain Pass argument combined with the so-called "monotonicity trick", as well as on a priori estimates for the Palais-Smale sequences. Finally, we establish properties of the solitons such us exponential decay at infinity and analyticity.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
ANR Project :
Collections :
Source :
Submission date :
2025-01-24T15:54:45Z
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