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We consider one- and two-dimensional (1D and 2D) optical or matter-wave mediawith a maximum of the local self-repulsion strength at the center, and aminimum at periphery. If the central area is broad enough, it supports groundstates in the form of flat-floor \textquotedblleft bubbles", and topologicalexcitations, in the form of dark solitons in 1D and vortices with windingnumber $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modeswere not previously considered in this setting. The ground and excited statesare accurately approximated by the Thomas-Fermi expressions. The 1D and 2Dbubbles, as well as vortices with $m=1$, are completely stable, while the darksolitons and vortices with $m=2$ have nontrivial stability boundaries in theirexistence areas. Unstable dark solitons are expelled to the periphery, whileunstable double vortices split in rotating pairs of unitary ones. Displacedstable vortices precess around the central point.

Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media