Global bifurcation of vortex and dipole solutions in Bose-Einstein condensates

The Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) with symmetric harmonic trap is given in (1). Periodic solutions of (1) play an important role in the understanding of the long term behavior of its solutions. In this note we prove the existence of several global branches of solutions to (1) among which there are vortex solutions and dipole solutions.