BIFURCATIONS OF MULTI-VORTEX CONFIGURATIONS IN ROTATING BOSE-EINSTEIN CONDENSATE

Global bifurcations along the family of radially symmetric vortices are analyzed for the Gross-Pitaevskii equation with a symmetric harmonic potential and a chemical potential under the steady rotation. The families are constructed in the small-amplitude limit when the chemical potential is close to an eigenvalue of the Schrodinger operator for a quantum harmonic oscillator. Each bifurcation results in the disappearance of a pair of negative eigenvalues in the Hessian operator at the radially symmetric vortex. The distributions of vortices in the bifurcating families are analyzed by using symmetries of the Gross-Pitaevskii equation and the zeros of Hermite-Gauss eigenfunctions. The vortex configurations that can be found in the bifurcating families are the asymmetric vortex, the asymmetric vortex pair, and the vortex polygons.