Stable three-dimensional spatially modulated vortex solitons in Bose-Einstein condensates

TL;DR

This paper demonstrates the existence and stability of three-dimensional spatially localized vortex solitons, including rotating azimuthons, in Bose-Einstein condensates, supported by numerical solutions and stability analysis.

Contribution

The study provides the first numerical solutions and stability analysis of 3D vortex solitons and azimuthons in BECs, revealing their continuous family and stability conditions.

Findings

3D azimuthon solutions form a continuous family parametrized by angular velocity.

Stable azimuthons exist with sufficiently large phase modulational depth.

Numerical simulations confirm the stability of these vortex solitons.

Abstract

We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show that the 3D azimuthon solutions exist as a continuous family parametrized by the angular velocity (or, equivalently, the modulational depth). By a linear stability analysis we show that 3D azimuthons with a sufficiently large phase modulational depth can be stable. The results are confirmed by direct numerical simulations of the Gross-Pitaevskii equation.