  Vortex rings are ubiquitous in fluids, with smoke rings being a familiar
example. The interaction of multiple vortex rings produces complex dynamical
behaviour, such as the leapfrogging motion first analysed by Helmholtz more
than a century and a half ago. Here we report on numerical investigations of
vortex ring dynamics in a different setting from fluids, namely, as solutions
of the Landau-Lifshitz equation that models the evolution of the local
magnetization in a ferromagnetic medium. We present the results of the first
study on the dynamics of interacting magnetic vortex rings and provide a novel
link between fluids and magnetism, by showing that a range of phenomena
familiar in fluids are reproduced in ferromagnets. This includes the
leapfrogging motion of a pair of vortex rings and evidence for the chaotic
dynamics of a trio of rings.
