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We demonstrate stable and metastable vortex-bright solitons in athree-dimensional spin-orbit-coupled three-component hyperfine spin-1Bose-Einstein condensate (BEC) using numerical solution and variationalapproximation of a mean-field model. The spin-orbit coupling providesattraction to form vortex-bright solitons in both attractive and repulsivespinor BECs. The ground state of these vortex-bright solitons is axiallysymmetric for weak polar interaction. For a sufficiently strong ferromagneticinteraction, we observe the emergence of a fully asymmetric vortex-brightsoliton as the ground state. We also numerically investigate moving solitons.The present mean-field model is not Galilean invariant, and we use aGalilean-transformed mean-field model for generating the moving solitons.

Three-dimensional vortex-bright solitons in a spin-orbit coupled spin-$1$ condensate