  Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support
localized dark soliton excitations that show periodic density dynamics in real
space. In addition to the density feature, solitons also carry a localized
pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic
results for Rashba-type spin-orbit coupling and spin-invariant interactions
predict a conserved magnitude and precessional motion for the soliton
magnetization that allows for the simulation of spin-related geometric phases
recently seen in electronic transport measurements.
