Topological vortices in the modified two-dimensional Gross-Pitaevskii theory

It is shown that there exists an elementary vortex topological current in the modified two-dimensional Gross-Pitaevskii theory. An explicit expression for the vortex velocity field as a function of the order parameter is derived. The evolution of vortices is studied from the topological properties of the order parameter field. It is found that vortices generate or annihilate at the limit points and encounter, split, or merge at the bifurcation points of the order parameter field psi.