  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.
