Hyperbolic geometric asymptotics

Article type: Research Article

Authors: Alber, Mark S.

Affiliations: Department of Mathematics, University of Notre Dame, P.D. Box 398, Notre Dame, IN 46556, USA

Abstract: Geometric asymptotics in hyperbolic case are investigated. In particular, semiclassical solutions (modes) of the stationary Schrödinger equation corresponding to the Jacobi problem on geodesics on n-dimensional hyperboloids are constructed in the form of the multi-valued functions of several complex variables (geometric asymptotics) on the Jacobi varieties. Then a special limiting process (collapsing construction) is used in order to obtain from this problem reflected and diffracted modes for investigating geometric theory of diffraction.

DOI: 10.3233/ASY-1991-5205

Journal: Asymptotic Analysis, vol. 5, no. 2, pp. 161-172, 1991