  It was recently found that the spin-orbit (SO) coupling can help to create
stable matter-wave solitons in spinor Bose-Einstein condensates in the
two-dimensional (2D) free space. Being induced by external laser illumination,
the effective SO coupling can be applied too in a spatially confined area.
Using numerical methods and the variational approximation (VA), we build
families of 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types, and
explore their stability, assuming that the SO-coupling strength is confined in
the radial direction as a Gaussian. The most essential result is
identification, by means of the VA and numerical methods, of the minimum size
of the spatial confinement for which the 2D system maintains stable solitons of
the SV and MM types.
