  The soft-core boson system is one of the simplest models of supersolids,
which have both off-diagonal long-range order (Bose-Einstein condensation) and
diagonal long-range order (crystalline order). Although this model has been
studied from various points of view, studies of the stability of
current-flowing states are lacking. Solving the Gross-Pitaevskii and Bogoliubov
equations, we obtain excitation spectra in superfluid, supersolid, and stripe
phases. On the basis of the results of the excitation spectra, we present a
stability phase diagram that shows the region of the metastable superflow
states for each phase.
