Singularities of solutions to Schrodinger equation on scattering manifold

Details Singularities of solutions to Schrodinger equation on scattering manifold Singularities of solutions to Schrodinger equation on scattering manifold

2007-11-21

arxiv.org/abs/0711.3258v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e., noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in terms of the initial condition and the classical scattering maps under the nontrapping condition. Our result is closely related to a recent work by Hassell and Wunsch, though our model is more general and the method, which relies heavily on scattering theoretical ideas, is simple and quite different. In particular, we use Egorov-type argument in the standard pseudodifferential symbol classes, and avoid using Legendre distributions. In the proof, we employ a microlocal smoothing property in terms of the radially homogenous wave front set, which is more precise than the preceding results.

Affiliated with

Also associated with

No associations

Rating

Singularities of solutions to Schrodinger equation on scattering manifold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singularities of solutions to Schrodinger equation on scattering manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singularities of solutions to Schrodinger equation on scattering manifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-413800