LAUSR

We investigate the vortex dynamic behavior of Bose-Einstein condensate in a spatially two-dimensional harmonic potential with spatially modulated defocusing nonlinearity. Kinds of exact vortex solutions of the Gross-Pitaevskii equation are obtained by designing various laser potentials which can be experimentally realized. In particular, we demonstrate that the spatially modulated defocusing nonlinearity supports stable vortex clusters. For the stationary vortex solutions, the vortex clusters are dynamically stable, and the circulation direction of each vortex and vortex core positions remain unchanged. However, for the non-stationary vortex solutions, stable and unstable vortex clusters exist. For the stable vortex clusters, the vortex core positions are constant during dynamical evolution, while the phase increase directions vary periodically. Additionally, corresponding to the unstable vortex clusters, vortices disappear and appear periodically in the condensate.