Hydrodynamics of a Multi-Component Bosonic Superfluid

We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under local equilibrium assumption and show that quantum pressure is generally present in nonuniform case. Our approach can be extended to systems long-range such as dipole-dipole by treating Hartree energy properly. For highly symmetric superfluid, we excitation spectrum except for density phonon, all other excitations are degenerate.The implication our results discussed.