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

Liangwei Zeng, Boris A. Malomed, Dumitru Mihalache, Yi Cai, Xiaowei Lu, Qifan Zhu, Jingzhen Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)815-830
Number of pages16
JournalNonlinear Dynamics
Volume106
Issue number1
DOIs
StatePublished - Sep 2021

Keywords

  • Flat-floor and flat-waist soltions
  • Inhomogeneous nonlinear media
  • Nonlinear Schrödinger equation
  • Precession of vortex solitons

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