Numerical computation of dark solitons of ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation
Auteur(s) :
De Laire, André [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Dujardin, Guillaume [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Universidad Autónoma de Madrid [UAM]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Dujardin, Guillaume [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Universidad Autónoma de Madrid [UAM]
Titre de la revue :
Journal of Nonlinear Science
Éditeur :
Springer Verlag
Date de publication :
2024-02
ISSN :
0938-8974
Mot(s)-clé(s) en anglais :
Gross-Pitaevskii equation
numerical methods
numerical computations
traveling waves
dark solitons
nonzero conditions at infinity
Nonlocal Schrödinger equation
numerical methods
numerical computations
traveling waves
dark solitons
nonzero conditions at infinity
Nonlocal Schrödinger equation
Discipline(s) HAL :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently [10]. Mathematically, ...
Lire la suite >The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently [10]. Mathematically, these solitons correspond to minimizers of the energy at fixed momentum and are orbitally stable. This paper provides a numerical method to compute approximations of such solitons for these types of equations, and provides actual numerical experiments for several types of physically relevant nonlocal potentials. These simulations allow us to obtain a variety of dark solitons, and to comment on their shapes in terms of the parameters of the nonlocal potential. In particular, they suggest that, given the dispersion relation, the speed of sound and the Landau speed are important values to understand the properties of these dark solitons. They also allow us to test the necessity of some sufficient conditions in the theoretical result proving existence of the dark solitons.Lire moins >
Lire la suite >The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently [10]. Mathematically, these solitons correspond to minimizers of the energy at fixed momentum and are orbitally stable. This paper provides a numerical method to compute approximations of such solitons for these types of equations, and provides actual numerical experiments for several types of physically relevant nonlocal potentials. These simulations allow us to obtain a variety of dark solitons, and to comment on their shapes in terms of the parameters of the nonlocal potential. In particular, they suggest that, given the dispersion relation, the speed of sound and the Landau speed are important values to understand the properties of these dark solitons. They also allow us to test the necessity of some sufficient conditions in the theoretical result proving existence of the dark solitons.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
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