  We investigate the dynamics of a spinor Bose-Einstein condensate which is
governed by an optically induced non-Abelian gauge potential. Using a ring
shaped trap to confine the atoms and a hydrodynamic ansatz, nonlinear Josephson
type equations are found to describe the system. The degenerate eigenstates
which show rotation are solved exactly. We consider a homogenous filled ring
and observe population dynamics between the two quasi-spin components but also
space dependent Josephson oscillations. Stable mass currents can be observed
which are induced by the constant non-Abelian effective magnetic field in the
limit of weak interactions. For strong interactions the appearance of
two-component dark soliton-like objects are observed.
