Scattering and leapfrogging of vortex rings in a superfluid
  The dynamics of vortex ring pairs in the homogeneous nonlinear Schr\"odinger equation is studied. The generation of numerically-exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the Biot-Savart law. 
R. M. Caplan, J. D. Talley, R. Carretero-Gonzalez, and P.G. Kevrekidis
cond-mat.other nlin.PS physics.flu-dyn