Leapfrogging vortex rings for the three dimensional Gross-Pitaevskii equation
Robert L. Jerrard, Didier Smets
TL;DR
This paper rigorously derives the leapfrogging motion of vortex rings within the three-dimensional Gross-Pitaevskii equation, extending classical fluid dynamics concepts to quantum fluid models.
Contribution
It provides the first rigorous mathematical derivation of leapfrogging vortex rings for the 3D Gross-Pitaevskii equation, bridging classical and quantum fluid dynamics.
Findings
Derivation of leapfrogging vortex ring motion in the Gross-Pitaevskii framework
Extension of classical vortex dynamics to quantum fluids
Mathematical validation of vortex ring behavior in Bose-Einstein condensates
Abstract
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.
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