Exact exact solutions of the Gross-Pitaevskii equation for stable vortex modes

TL;DR

This paper derives exact solutions for vortex modes in 2D Bose-Einstein condensates modeled by the Gross-Pitaevskii equation, revealing new stable vortex states with higher vorticity and radial excitations.

Contribution

It provides the first exact solutions for stable vortex modes with vorticity S≥2 and higher-order radial states in 2D BEC models with spatially modulated nonlinearity.

Findings

Exact vortex solutions for S≥2 are constructed.

New stable higher-order radial vortex states are identified.

The number of vortex-soliton modes relates to the spectrum of a linear Schrödinger equation.

Abstract

We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schr\"{o}dinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with vorticity $S\geq 2$ and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.