  We investigate the stationary vortex solutions in two-dimensional (2D) Rashba
spin-orbit (SO) coupled spin-1 Bose-Einstein condensate (BEC). By introducing
the generalized momentum operator, the linear version of the system can be
solved exactly and its solutions are a set of the Bessel vortices. Based on the
linear version solutions, the stationary vortex solutions of the full nonlinear
system are constructed and determined entirely by the variational
approximation. The results show that the variational results are in good
agreement with the numerical ones. By means of the variational results, the
vortex ground state phase-transition between the stationary vortex solutions,
stability, and the unit Bloch vector textures are discussed in detail. The
results have the potential to be realized in experiment.
