  We report the numerical realization and demonstration of robustness of
certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial
dimensions with non-trivial topological charge in one of the components. In
particular, we identify a stable symbiotic state in which a higher-dimensional
bright soliton exists even in a homogeneous setting with defocusing
interactions, as a result of the effective potential created by a stable vortex
in the other component. The resulting vortex-bright solitary waves, which
naturally generalize the recently experimentally observed dark-bright solitons,
are examined both in the homogeneous medium and in the presence of parabolic
and periodic external confinement and are found to be very robust.
