Author: J Cuevas (pdf 1.3 Mb).
With G James, PG Kevrekidis, KJH Law and F Palmero

Abstract: 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.

7th International Conference of Numerical Analysis and Applied Mathematics, Rethymno - Crete (Greece), September 18-22, 2009.
Talk.