Title: Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates,
Abstract: The Lowest Landau Level (LLL) equation emerges as an accurate approximation
for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in
two-dimensional isotropic harmonic traps in the limit of weak interactions.
Building on recent developments in the field of spatially confined extended
Hamiltonian systems, we find a fully nonlinear solution of this equation
representing periodically modulated precession of a single vortex. Motions of
this type have been previously seen in numerical simulations and experiments at
moderately weak coupling. Our work provides the first controlled analytic
prediction for trajectories of a single vortex, suggests new targets for
experiments, and opens up the prospect of finding analytic multi-vortex
solutions.