Three-dimensional hybrid vortex solitons

TL;DR

This paper demonstrates the existence and stability of complex three-dimensional vortex solitons in media with spatially varying repulsive nonlinearity, including hybrid and analytically exact solutions, with potential applications in Bose-Einstein condensates.

Contribution

It introduces novel 3D vortex states supported by specific nonlinear profiles, including hybrid and exact analytical solutions, expanding the understanding of vortex solitons in nonlinear media.

Findings

Identification of stable hybrid vortex states

Derivation of exact analytical solutions for 3D vortex solitons

Mapping of stability regions for various vortex configurations

Abstract

We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity base. The analysis reveals stability regions for symmetric, antisymmetric, and hybrid states. In addition, bead-shaped modulation profiles give rise to the first example of exact analytical solutions for stable three-dimensional vortex solitons. The predicted states may be realized in media with a controllable cubic nonlinearity, such as Bose-Einstein condensates.