  We compute the low-energy classical differential scattering cross-section for
BPS $SU(2)$ magnetic monopoles using the geodesic approximation to the actual
dynamics and 16K parallel processors on a CM2. Numerical experiments suggest
that the quantum BPS magnetic monopole differential cross-section is
well-approximated by the classical BPS magnetic monopole differential
cross-section. In particular, the expected quantum interference effects for
bosons at scattering angle $\theta=\pi/2$ (CoM frame) are contradicted
numerically. We argue that this is due to the topology of the classical
configuration space for these solitons. We also study the scattering and
bounded classical motions of BPS dyons and their global structure in phase
space by constructing `escape plots'. The escape plots contain a surprising
amount of structure, and suggest that the classical dynamics of two BPS $SU(2)$
magnetic monopoles is chaotic and that there are closed and bounded two dyon
motions with isolated energies.
