By the same authors

On Some Configurations of Oppositely Charged Trapped Vortices in the Plane

Research output: Contribution to journalArticlepeer-review

Published copy (DOI)


  • Emilie Dufresne
  • Heather A Harrington
  • Panayotis G Kevrekidis
  • Paolo Tripoli
  • Jonathan D. Hauenstein


Publication details

JournalAdvances in Applied Mathematics
DateSubmitted - 26 Oct 2018
DateAccepted/In press - 4 Aug 2020
DateE-pub ahead of print (current) - 16 Dec 2020
Early online date16/12/20
Original languageEnglish


Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. The use of invariants and symmetries enables deducing a set of equations in elementary symmetric polynomials, which can then be fully solved via computational algebra packages within Maple. We retrieve a number of previously identified configurations, including collinear ones and polygonal (e.g. quadrupolar and hexagonal) ones. However, importantly, we also retrieve a configuration with 4 positive charges and 2 negative ones which is unprecedented, to the best of our knowledge, in BEC studies. We corroborate these predictions via numerical computations in the fully two-dimensional PDE system of the Gross-Pitaevskii type which characterizes the BEC at the mean-field level.

Bibliographical note

29 pages, 3 figures
© 2020 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

    Research areas

  • Bose-Einstein condensates, standing wave vortex configurations in the plane, symbolic computational methods, Invariant theory

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