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P.G. Kevrekidis and D.E. Pelinovsky

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On the characterization of vortex configurations in the steady rotating Bose-Einstein condensates

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Proceedings of the Royal Society of London A 473 (2017) 20170602 (17 pages)

**Abstract:**

Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions
of a system of ordinary differential equations (ODE) for dynamics of one and two
individual vortices in the rotating BECs with those of the partial differential equation (PDE).
In particular, we characterize orbitally stable vortex configurations in a symmetric harmonic
trap due to a cubic repulsive interaction and the steady rotation. The ODE system is analyzed
in details and the PDE model is approximated numerically. Good agreement between
the two models is established in the semi-classical (Thomas-Fermi) limit that corresponds to
the BECs at the large chemical potentials.

**Keywords:**

Gross-Pitaevskii equation, rotating vortices, harmonic potentials, semi-classical limit,
vortex ODE models, energy minimization, stability of vortices.