Title :

Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation

Author(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]

Journal title :

Journal of Nonlinear Science

Publisher :

Springer Verlag

Publication date :

2024-02

ISSN :

0938-8974

English keyword(s) :

Gross-Pitaevskii equation
numerical methods
numerical computations
traveling waves
dark solitons
nonzero conditions at infinity
Nonlocal Schrödinger equation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [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, ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL