Ring dark solitons in three-dimensional Bose-Einstein condensates

Wenlong Wang, P. G. Kevrekidis, and Egor Babaev
Phys. Rev. A 100, 053621 – Published 25 November 2019

Abstract

In this work we present a systematic study of the three-dimensional extension of the ring dark soliton, examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging, such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semianalytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov–de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.

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  • Received 23 July 2019

DOI:https://doi.org/10.1103/PhysRevA.100.053621

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalNonlinear Dynamics

Authors & Affiliations

Wenlong Wang1,*, P. G. Kevrekidis2,†, and Egor Babaev1

  • 1Department of Physics, Royal Institute of Technology, Stockholm, SE-106 91, Sweden
  • 2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

  • *wenlongcmp@gmail.com
  • kevrekid@math.umass.edu

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Issue

Vol. 100, Iss. 5 — November 2019

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