Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2017

Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

Résumé

In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |ψ| 2 ψ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H 1 2 (R 2 , C 2) → L 4 (R 2 , C 4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments. Contents
Fichier principal
Vignette du fichier
ShootingDirac.pdf (415.13 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01540930 , version 1 (16-06-2017)
hal-01540930 , version 2 (28-06-2017)

Identifiants

Citer

William Borrelli. Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity. Journal of Differential Equations, 2017. ⟨hal-01540930v2⟩
209 Consultations
296 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More