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.
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