标题： 均匀地板气泡、暗孤子和涡旋在非均匀非线性介质中的稳定化 显示英文标题

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

摘要： 我们考虑具有中心局部自排斥强度最大、边缘最小的一维和二维（1D 和 2D）光学或物质波介质。如果中心区域足够宽，它会以平底\textquotedblleft 泡泡的形式支持基态，以及以一维暗孤子和二维绕数为$m$的涡旋形式支持拓扑激发态。与亮孤子不同，非局域泡和暗态在此设置中之前未被考虑过。基态和激发态由 Thomas-Fermi 表达式准确近似。一维和二维泡以及绕数为$m=1$的涡旋是完全稳定的，而暗孤子和绕数为$m=2$的涡旋在其存在区域内具有非平凡的稳定性边界。不稳定的暗孤子会被驱赶到边缘，而不稳定的双涡旋会分裂成旋转的单位涡旋对。位移的稳定涡旋围绕中心点进动。 显示英文摘要

摘要： 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 \textquotedblleft 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 split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.