Extended Lagrangian approach for the defocusing Non-Linear Schrödinger equation - Université Toulouse 3 Accéder directement au contenu
Article Dans Une Revue Studies in Applied Mathematics Année : 2018

Extended Lagrangian approach for the defocusing Non-Linear Schrödinger equation

Résumé

We study the defocusing Non-Linear Schrödinger (NLS) equation written in hydrodynamic form through the Madelung transform. From the mathematical point of view, the hydrodynamic form can be seen as the Euler-Lagrange equations for a Lagrangian submitted to a differential constraint corresponding to the mass conservation law. The dispersive nature of NLS equation poses some major numerical challenges. The idea is to introduce a two-parameter family of extended Lagrangians, depending on a greater number of variables, whose Euler-Lagrange equations are hyperbolic and accurately approximate NLS equation in a certain limit. The corresponding hyperbolic equations are studied and solved numerically using Godunov type methods. Comparison of exact and asymptotic solutions to the NLS equation ('grey' solitons and dispersive shocks) and the corresponding numerical solutions to the extended system was performed. A very good accuracy of such a hyperbolic approximation was observed.
Fichier principal
Vignette du fichier
Article_NLS_2.pdf (706.58 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01779915 , version 1 (27-04-2018)

Identifiants

Citer

F Dhaouadi, Nicolas Favrie, S. Gavrilyuk. Extended Lagrangian approach for the defocusing Non-Linear Schrödinger equation. Studies in Applied Mathematics, 2018, ⟨10.1111/sapm.12238⟩. ⟨hal-01779915⟩
160 Consultations
344 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More