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We have studied collective modes of quasi-2D Bose-Einstein condensates withmultiply-charged vortices using a variational approach. Two of the fourcollective modes considered exhibit coupling between the vortex dynamics andthe large-scale motion of the cloud. The vortex presence causes a shift in allfrequencies of collective modes even for the ones that do not coupledynamically with the vortex-core. The coupling between vortex and large-scalecollective excitations can induce the multi-charged vortex to decay intosingly-charged vortices with the quadrupole mode being one possible channel forsuch a decay. Therefore a thorough study was done about the possibility toprevent the vortex decay by applying a Gaussian potential with its widthproportional to the vortex-core radius and varying its height. In such way, wecreated a stability diagram of height versus interaction strength which hasstable regions due the static Gaussian potential. Furthermore, by using asinusoidal time-modulation around the average height of the Gaussian potential,we have obtained a diagram for the parametric resonance which can prevent thevortex decay in regions where static potential can not.

Stability change of a multi-charged vortex due to coupling with quadrupole mode