Supersolid and the non-uniform condensate

We construct a model of non-uniform condensate having a spatially modulated complex order parameter that makes it kinematically an x-ray solid, i.e., a real mass density wave, but one admitting an associated superfluid flow. Intrinsic to this state is a non-classical translational inertia which we derive for the case of a potential flow. Connection to the non-classical rotational inertia observed in recent experiments on solid helium-4 is discussed. Our semi-phenomenological treatment suggests a flow-induced supersolid-to-superdfluid transition.