  Macroscopic derivation of the entrainment in in a Andreev-Lifshitz Supersolid
induced by a surface elastic wave propagating along the flexible interface is
conducted by considering the nonlinear coupling between the interface and the
rarefaction effect. We obtain the critical bounds for zero-volume-flow-rate
states corresponding to specific rarefaction measure and wave number which is
relevant to the rather small critical velocity of supersolid flows reported by
Kim and Chan.
