  Using a (1+2)-dimensional boson-vortex duality between non-linear
electrodynamics and a two-component compressible Bose-Einstein condensate (BEC)
with spin-orbit (SO) coupling, we obtain generalised versions of the
hydrodynamic continuity and Euler equations where the phase defect and
non-defect degrees of freedom enter separately. We obtain the generalised
Magnus force on vortices under SO coupling, and associate the linear
confinement of vortices due to SO coupling with instanton fluctuations of the
dual theory.
