  In this work, we generalize the two-fluid theory to a superfluid system with
anisotropic effective masses along different principal axis directions. As a
specific example, such a theory can be applied to spin-orbit coupled
Bose-Einstein condensate (BEC) at low temperature. The normal density from
phonon excitations and the second sound velocity are obtained analytically.
Near the phase transition from the plane wave to zero-momentum phases, due to
the effective mass divergence, the normal density from phonon excitation
increases greatly, while the second sound velocity is suppressed significantly.
With quantum hydrodynamic formalism, we give unified derivations for suppressed
superfluid density and Josephson relation. At last, the momentum distribution
function and fluctuation of phase for the long wave length are also discussed.
