  We demonstrate the existence of one and two-dimensional bright solitons in
the Bose-Einstein condensate with repulsive dipole-dipole interactions induced
by a combination of dc and ac polarizing fields, oriented perpendicular to the
plane in which the BEC is trapped, assuming that the strength of the fields
grows in the radial ($r$) direction faster than $r^{3}$. Stable tightly
confined 1D and 2D fundamental solitons, twisted solitons in 1D, and solitary
vortices in 2D are found in a numerical form. The fundamental solitons remain
robust under the action of an expulsive potential, which is induced by the
interaction of the dipoles with the polarizing field. The confinement and
scaling properties of the soliton families are explained analytically. The
Thomas-Fermi approximation is elaborated for fundamental solitons. The mobility
of the fundamental solitons is limited to the central area. Stable 1D even and
odd solitons are also found in the setting with a double-well modulation
function, along with a regime of Josephson oscillations.
