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We demonstrate the existence of one and two-dimensional bright solitons inthe Bose-Einstein condensate with repulsive dipole-dipole interactions inducedby a combination of dc and ac polarizing fields, oriented perpendicular to theplane in which the BEC is trapped, assuming that the strength of the fieldsgrows in the radial ($r$) direction faster than $r^{3}$. Stable tightlyconfined 1D and 2D fundamental solitons, twisted solitons in 1D, and solitaryvortices in 2D are found in a numerical form. The fundamental solitons remainrobust under the action of an expulsive potential, which is induced by theinteraction of the dipoles with the polarizing field. The confinement andscaling properties of the soliton families are explained analytically. TheThomas-Fermi approximation is elaborated for fundamental solitons. The mobilityof the fundamental solitons is limited to the central area. Stable 1D even andodd solitons are also found in the setting with a double-well modulationfunction, along with a regime of Josephson oscillations.

Matter-wave solitons supported by field-induced dipole-dipole repulsion with a spatially modulated strength