Propagation of the homogeneous wave front set for Schrödinger equations

Abstract

In this paper we study the propagation of singularity for Schrödinger-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≠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.