Vortex solutions in atomic Bose-Einstein condensates via the Adomian Decomposition Method

TL;DR

This paper applies the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation, providing analytical vortex solutions in Bose-Einstein condensates that closely match numerical results.

Contribution

It introduces a novel analytical approach using the Adomian Decomposition Method for vortex solutions in BECs, extending the solution techniques for the Gross-Pitaevskii equation.

Findings

Analytical vortex solutions agree well with numerical solutions

Power series solutions effectively describe vortex dynamics

Method applicable to different potential types

Abstract

We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions of the vortex equation are expressed in the form of infinite power series. The power series representations are compared with the exact numerical solutions of the Gross-Pitaevskii equation for the uniform and the harmonic potential, respectively. We find that there is a good agreement between the analytical and the numerical results.