  We consider the motion of superconducting vortices and skyrmions on a square
substrate near the first commensurate matching field. Slightly above
commensuration, a series of dynamic phases appear including interstitial flow,
and there is a transition from fluid flow to soliton flow that generates
negative differential conductivity. Slightly below commensuration, vacancy
depinning occurs. The dynamic phase transitions produce features in the
velocity-force curves, differential mobility, and velocity fluctuations. When a
Magnus force is also present, as in certain superconducting vortex or skyrmion
systems, there is an expansion of the fluid state, and at lower drives there is
a finite Hall angle in the fluid phase but a vanishing Hall angle in the
soliton phase, giving rise to a reentrant Hall effect. We also find a regime
where the Hall motion of the particles exhibits the same dynamic phases,
including soliton motion at a finite angle that produces negative differential
conductivity in the Hall response but not in the longitudinal response. Our
results suggest that vortices driven over periodic pinning may be an ideal
system for determining if a vortex Hall effect is occurring and would also be
relevant for skyrmions at smaller Magnus forces.
