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

We have studied collective modes in the presence of a multi-charged vortex using the variational method which couples the vortex-core dynamics with collective excitations. We found four collective modes where only two of them present this coupling, and an extra independent rotational motion of the asymmetric vortex core. The vortex presence causes a shift in all frequencies of collective modes even for the collective modes that do not couple dynamically with the vortex-core. The coupling of vortex with collective excitations can induce the multi-charged vortex to decay into singly-charged vortices being the quadrupole mode one possible channel for such a decay. Therefore we have done a complete study of the possibility to prevent the vortex decay by applying a Laguerre-Gauss potential with its width proportional to the vortex-core radius and varying its amplitude. In such way, we created a diagram of amplitude versus interaction strength which has stable regions due the static Laguerre-Gauss potential. Furthermore, by using a sinusoidal time-modulation of this potential amplitude we have obtained a diagram for the parametric resonance which can prevent the vortex decay in regions where static potential can not.