Stable matter-wave solitons in the vortex core of a uniform condensate

We demonstrate a stable, mobile, dipolar or nondipolar three-dimensional matter-wave soliton in the vortex core of a uniform nondipolar condensate. All intra-and inter-species contact interactions can be repulsive for a strongly dipolar soliton. For a weakly dipolar or nondipolar soliton, the intra-species contact interaction in the soliton should be attractive for the formation of a compact soliton. The soliton can propagate with a constant velocity along the vortex core without any deformation. Two such solitons undergo a quasi-elastic collision at medium velocities. We illustrate the findings using realistic interactions in a mean-field model of binary Rb-87-Rb-85 and Rb-87-Dy-164 systems.