Propagation of the homogeneous wave front set for Schrodinger equations

In this paper we study the propagation. of singularity for Schrodinger-type equations with variable coefficients. We introduce a new notion of wave propagation set, the homogeneous wave front set, which propagates along straight lines with finite speed away from x not equal 0. Then we show that it is related to the wave front set in a natural way. These results may be considered as a refinement of the microlocal smoothing property of Craig, Kappeler, and Strauss under more general assumptions.