Ring dark solitons in three-dimensional Bose-Einstein condensates

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 semi-analytical 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.

12 pages, 11 figures

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Cited by in corpus (7)

• Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates
• Deflation-based Identification of Nonlinear Excitations of the 3D Gross--Pitaevskii equation
• Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Systematic vector solitary waves from their linear limits in one-dimensional $n$-component Bose-Einstein condensates
• Shock Waves in a Superfluid with Higher-Order Dispersion
• Finding the stable mechanism of ring solitons in two-dimensional Fermi superfluids