  We study the dynamics of vortices in ideal and weakly interacting
Bose-Einstein condensates using a Ritz minimization method to solve the
two-dimensional Gross-Pitaevskii equation. For different initial vortex
configurations we calculate the trajectories of the vortices. We find
conditions under which a vortex-antivortex pair annihilates and is created
again. For the case of three vortices we show that at certain times two
additional vortices may be created, which move through the condensate and
annihilate each other again. For a noninteracting condensate this process is
periodic, whereas for small interactions the essential features persist, but
the periodicity is lost. The results are compared to exact numerical solutions
of the Gross-Pitaevskii equation confirming our analytical findings.
