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

We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor bubbles, and topological excitations, in the form of dark solitons in 1D and vortices with winding number m in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with m = 1, are completely stable, while the dark solitons and vortices with m = 2 have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices are split into rotating pairs of unitary ones. Displaced stable vortices precess around the central point.

Automated summary

This study explores one- and two-dimensional optical or matter-wave media with varying self-repulsion strengths and identifies stable ground states and topological excitations like bubbles, dark solitons, and vortices. The Thomas-Fermi expressions provide accurate approximations for these states, showing stability boundaries for different types of solitons and vortices in different dimensions. The findings reveal interesting dynamics of stable and unstable solitons and vortices in these unique media configurations.