Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity

We study spatiotemporal three-dimensional bright solitons in optical media whose non-linear response includes third- and fifth-order terms. By means of numerical simulations, lower and upper stability and existence borders for the solitons without the internal ''spin'' are identified. Using the variational method based on two different trial functions and collating the results, we obtain approximate solutions for spinning (vortex) solitons. The presence of the lower stability border for both the zero-spin and spinning solitons is a drastic difference of the three-dimensional solitons from those in one and two dimensions. The results show that the corresponding stability and existence borders are chiefly determined by the spatial dimension, quite weakly depending on the soliton's ''spin.'' However, the energy of the spinning soliton is much larger than that of the zero-spin one.