Leapfrogging Vortex Rings for the Three Dimensional Gross-Pitaevskii Equation
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Leapfrogging motion of vortex rings sharing the same axis of symmetry was first predicted by Helmholtz in his famous work on the Euler equation for incompressible fluids. Its justification in that framework remains an open question to date. In this paper, we rigorously derive the corresponding leapfrogging motion for the axially symmetric three-dimensional Gross-Pitaevskii equation.
KeywordsVortex rings Leapfrogging Gross-Pitaevskii equation Incompressible Euler equation
The research of RLJ was partially supported by the National Science and Engineering Council of Canada under operating Grant 261955. The research of DS was partially supported by the Agence Nationale de la Recherche through the Project ANR-14-CE25-0009-01. Both authors wish to warmly thank a referee for his very careful reading of the manuscript and his judicious remarks.
- 1.Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions, U.S. Government Printing Office, Washington D.C. (1964)Google Scholar
- 8.Helmholtz, H.: (translated by P.G. Tait) On the integrals of the hydrodynamical equations which express vortex-motion. Phil. Mag. 33, 485–512 (1867)Google Scholar