  It was found that spatially confined spin-orbit (SO) coupling, which can be
induced by illuminating Bose-Einstein condensates (BECs) with a Gaussian laser
beam, can help trap a spinor Bose gas in multi-dimensional space. Previous
works on this topic were all based on a Boson gas featuring an attractive
interaction. In this paper, we consider the trapping effect in the case in
which the Boson gas features a repulsive interaction. After replacing the
repulsive effect, stable excited modes of semi-vortex (SV) type and mixed-mode
(MM) type, which cannot be created in a boson gas with attractive interactions,
can be found in the current setting. The trapping ability and the capacity of
the confined SO coupling versus the degree of the repulsive strength as well as
the order of the excited mode are systematically discussed firstly through the
paper. Moreover, the stability of the nonlinear mode trapped in this system
with a moving reference frame is also discussed. Unlike the system with
homogeneous SO coupling, two different types of stationary mobility modes can
be stabilized when the SO coupling moves in the x- and y- directions,
respectively. This finding indicates that the system with moving confined SO
coupling features a typical anisotropic character that differs from the system
with moving homogeneous SO coupling.
