  We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and
three-dimensional (3D) spatiotemporal optical soliton in the core of an optical
vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton
can propagate with a constant velocity along the vortex core without any
deformation. Stability of the soliton under a small perturbation is established
numerically. Two such solitons moving along the vortex core can undergo a
quasi-elastic collision at medium velocities. Possibilities of forming such a
2D spatial soliton in the core of a vortical beam are discussed.
