  By developing a hydrodynamic formalism, we investigate the expansion dynamics
of the single-minimum phase of a binary spin-orbit coupled Bose-Einstein
condensate, after releasing from an external harmonic trap. We find that the
expansion of the condensate along the direction of the spin-orbit coupling is
dramatically slowed down near the transition between the single-minimum phase
and the plane-wave phase. Such a slow expansion, resembling a form of an
effective localization, is due to the quenching of the superfluid motion which
results in a strong increase of the effective mass. In the single-minimum phase
the anisotropic expansion of the Bose gas, which is spin balanced at
equilibrium, is accompanied by the emergence of a local spin polarization. Our
analytic scaling solutions emerging from hydrodynamic picture are compared with
a full numerical simulation based on the coupled Gross-Pitaevskii equations.
