Dynamical systems admitting normal shift and wave equations

Details Dynamical systems admitting normal shift and wave equations Dynamical systems admitting normal shift and wave equations

2001-08-23

arxiv.org/abs/math/0108158v1

Mathematics

Differential Geometry

AmSTeX, 16 pages, amsppt style

Scientific paper

High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton equations being special case for Newton's equations. In simplest cases (e. g. light propagation in isotropic non-homogeneous refracting media) the dynamics of points preserves orthogonality of wave front and rays. This property was generalized in the theory of dynamical systems admitting normal shift of hypersurfaces. In present paper inverse problem is studied, i. e. the problem of reconstructing wave equation corresponding wave front dynamics for which is described by Newtonian dynamical system admitting normal shift of hypersurfaces in Riemannian manifold.

Affiliated with

Also associated with

No associations

Rating

Dynamical systems admitting normal shift and wave equations 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 Dynamical systems admitting normal shift and wave equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical systems admitting normal shift and wave equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190116