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We predict the existence of stable fundamental and vortical bright solitonsin dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipoleinteractions (DDI). The condensate is trapped in the 2D plane with the help ofthe repulsive contact interactions whose local strength grows $\sim r^{4}$ fromthe center to periphery, while dipoles are oriented perpendicular to theself-trapping plane. The confinement in the perpendicular direction is providedby the usual harmonic-oscillator potential. The objective is to extend therecently induced concept of the self-trapping of bright solitons and solitaryvortices in the pseudopotential, which is induced by the repulsive localnonlinearity with the strength growing from the center to periphery, to thecase when the trapping mechanism competes with the long-range repulsive DDI.Another objective is to extend the analysis for elliptic vortices and solitonsin an anisotropic nonlinear pseudopotential. Using the variationalapproximation (VA) and numerical simulations, we construct families ofself-trapped modes with vorticities $\ell =0$ (fundamental solitons), $\ell=1$, and $\ell =2$. The fundamental solitons and vortices with $\ell =1$ existup to respective critical values of the eccentricity of the anisotropicpseudopotential, being stable in the entire existence regions. The vorticeswith $\ell =2$ are stable solely in the isotropic model.

Vortical and fundamental solitons in dipolar Bose-Einstein condensates trapped in isotropic and anisotropic nonlinear potentials