Vortex solutions of the defocusing discrete nonlinear Schrödinger equation

Jesus Cuevas (1) , Guillaume James (2) , Panayotis G. Kevrekidis (3) , Kody Law (3)

1 Universidad de Sevilla = University of Seville
2 CASYS - Calculs Algébriques et Systèmes Dynamiques
3 Department of Mathematics and Statistics [University of Massachusetts]

We consider the existence, stability and dynamical evolution of dark vortex states in the two‐dimensional defocusing DNLS equation, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti‐continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Discrete defocusing vortices become unstable past a critical coupling strength and, subsequently feature a cascade of alternating stabilization‐destabilization windows for any finite lattice.

Mots clés: plasma nonlinear waves; Josephson effect; solitons

Domaines: Systèmes dynamiques [math.DS]

Jesus Cuevas, Guillaume James, Panayotis G. Kevrekidis, Kody Law. Vortex solutions of the defocusing discrete nonlinear Schrödinger equation. ICNAAM 2009 - 7th International Conference on Numerical Analysis and Applied Mathematics, Sep 2009, Rethymno, Crete, Greece. pp.135-138, ⟨10.1063/1.3241338⟩. ⟨hal-00769565⟩