Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate

TL;DR

This paper investigates the stability and transformation of solitons into vortex rings and vortices in a confined Bose-Einstein condensate, analyzing their profiles, bifurcations, and excitation spectra across different densities and velocities.

Contribution

It provides a detailed analysis of the instability modes and bifurcations leading to three-dimensional solitary waves in Bose-Einstein condensates, including energy-momentum relations.

Findings

Solitons become unstable at high densities and bifurcate into vortex rings and vortical structures.

Profiles of vortex rings and vortical solitons depend on propagation velocity.

A Lieb-type mode appears in the excitation spectrum at all densities.

Abstract

Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.