The antiferroelectric liquid crystalline phase and related ferrielectric phases exhibit a rich variety of physical behavior. Recently we have been examining the dynamics of these materials. For materials whose dielectric anisotropy Delta epsilon < 0, we find a critical threshold d.c. field E(th) in the Sm C-A* phase, above which solitary waves propagate rapidly along the layer direction. These solitary waves, which consist of ferroelectric regions propogating into an antiferroelectric sea, may be "frozen" in place by reducing the field to E(th), or forced to retreat by reducing the field to E < E(th).