  The dynamics of quantum vortices in a two-dimensional annular condensate are
considered by numerically simulating the Gross-Pitaevskii equation. Families of
solitary wave sequences are reported, both without and with a persistent flow,
for various values of interaction strength. It is shown that in the toroidal
geometry the dispersion curve of solutions is much richer than in the cases of
a semi-infinite channel or uniform condensate studied previously. In
particular, the toroidal condensate is found to have states of single vortices
at the same position and circulation that move with different velocities. The
stability of the solitary wave sequences for the annular condensate without a
persistent flow are also investigated by numerically evolving the solutions in
time. In addition, the interaction of vortex-vortex pairs and vortex-antivortex
pairs is considered and it is demonstrated that the collisions are either
elastic or inelastic depending on the magnitude of the angular velocity. The
similarities and differences between numerically simulating the
Gross-Pitaevskii equation and using a point vortex model for these collisions
are elucidated.
