The existence and stability properties of three-component vector solitons are studied. Linear stability analysis and numerical simulations show that when the power of vortex component is below a threshold, the fundamental component is stable, and the vortex components break up into dipole solitons; the dipole solitons originating from the vector solitons with total zero topological charges are very unique. While if the power of vortex components is higher than that threshold, all soliton components are unstable and break up into independent fundamental solitons. The instability of solitons with total zero topological charges is largely suppressed comparing to that of solitons with total nonzero topological charges.
The internal oscillation of spatial optical solitons in a cubic-quintic nonlinear medium is investigated systemically in their stability parameter region. Both internal oscillations of fundamental soliton and localized optical vortex soliton are determined. Internal modes with and without angular dependence are found. Our results show that internal oscillations exist only when the power of the soliton exceeds a threshold value. We also simulate the dynamics of soliton perturbed by internal modes. Numerical results show that internal oscillations induced by these modes are very robust. Some novel and interesting phenomena are discovered during the propagation process. Evolution of the perturbed state visually appears that the spatial soliton is uniformly (unevenly) breathing or rotating around the propagating axis periodically, the periods approximately equal to that of the internal oscillations.