Law, KKevrekidis, PG2024-04-262024-04-262010-01-01https://hdl.handle.net/20.500.14394/34111This is the pre-published version harvested from arXiv. The published version is located at http://prl.aps.org/abstract/PRL/v105/i16/e160405We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex–bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.Physical Sciences and Mathematicsarticle