Bifurcation of Vortex Density Current in Trapped Bose Condensates

Vortex density current in the Gross-Pitaevskii theory is studied. It is shown that the inner structure of the topological vortices can be classified by Brouwer degrees and Hopf indices of φ-mapping. The dynamical equations of vortex density current have been given. The bifurcation behavior at the critical points of the current is discussed in detail.