Vortex families near a spectral edge in the Gross-Pitaevskii equation   with a two-dimensional periodic potential
  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 Schroedinger 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. 
Tomas Dohnal and Dmitry Pelinovsky
nlin.PS