Dynamical evolution of two-dimensional Bose-Einstein condensates with harmonic potential

For Bose-Einstein condensates in two-dimensional scenarios, based on the Gross-Pitaevskii equation model with modified variational method, we studied first the oscillation and monotonic decay modes of isotropic vortices, then for asymmetric vortices, we studied the evolution modes with system isotropic potential and perturbations in angular direction. The corresponding stability of the rotating system with centrifugal potential is analyzed. We also calculated the criteria formula for the formation of sonic horizon corresponding to the occurrence of sonic black hole of isotropic Bose-Einstein condensate. For the asymmetric vortices evolution, we derived the corresponding oscillation and monotonously decay modes, calculated the stability features of the system under rotation, demonstrating the oscillation damping and monotonously accelerating effects for the system with rotating centrifugal potential. The theoretical results derived here can be used to guide the corresponding isotropic and asymmetric vortices experimental observation in two-dimensional Bose-Einstein condensates.