  We elaborate a method for the creation of two- and one-dimensional (2D and
1D) self-trapped modes in binary spin-orbit (SO)-coupled Bose-Einstein
condensates (BECs) with the contact repulsive interaction, whose local strength
grows fast enough from the center to periphery. In particular, an exact
semi-vortex (SV) solution is found for the anti-Gaussian radial-modulation
profile. The exact modes are included in the numerically produced family of SV
solitons. Other families, in the form of mixed modes(MMs), as well as excited
state of SVs and MMs, are produced too. While the excited states are unstable
in all previously studied models, they are partially stable in the present one.
In the 1D version of the system, exact solutions for the counterpart of the
SVs, namely, \textit{semi-dipole} solitons, are found too. Families of
semi-dipoles, as well as the 1D version of MMs, are produced numerically.
