Vortex-bright solitons in a spin-orbit coupled spin-$1$ condensate
We study the vortex-bright solitons in a quasi-two-dimensional spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein condensate (BEC) using variational method and numerical solution of a mean-field model. The ground state of these vortex-bright solitons is radially symmetric for weak ferromagnetic and polar interactions. For a sufficiently strong ferromagnetic interaction, we observe the emergence of an asymmetric vortex-bright soliton as the ground state. We also numerically investigate stable moving solitons and binary collision between them. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed model for generating the moving solitons. At low velocities, the head-on collision between two {\em in-phase} solitons results either in collapse or fusion of the soliton pair. On the other hand, in head-on collision, the two {\em out-of-phase} solitons strongly repel each other and trace back their trajectories before the actual collision. At low velocities, in a collision with an impact parameter, the {\em out-of-phase} solitons get deflected from their original trajectory like two rigid classical disks. These {\em out-of-phase solitons} behave like classical disks, and their collision dynamics is governed by classical laws of motion. However, at large velocities two SO-coupled spinor solitons, irrespective of phase difference, can pass through each other in a head-on collision like two quantum solitons.