  We study the conservative dynamics and stationary configurations of a
vortex-antivortex pair in a harmonically trapped two-dimensional Bose-Einstein
condensate. We establish the conceptual framework for understanding the
stationary states and the topological defect trajectories, through
considerations of different mechanisms of vortex motion and the bifurcation of
soliton-like stationary solutions. Our insights are based on Lagrangian-based
variational calculations, numerical solutions of both the time-dependent and
time-independent Gross-Pitaevskii equations, and exact solutions for the
non-interacting case.
