T. Dohnal and D. Pelinovsky

Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential

Physical Review E 85, 026605 (2012)

Abstract:
We examine numerically vortex families near band edges of the Bloch wave spectrum in the Gross–Pitaevskii equation with a two-dimensional periodic potential and in the discrete nonlinear Schrodinger equation. We show that besides vortex families that terminate at a small distance from the band edges via fold bifurcations there exist vortex families that are continued all way to the band edges.

Keywords:
vortices in periodic potentials, Gross-Pitaevskii equation, discrete nonlinear Schrodinger equations, numerical approximations