Abstract
In the paper a new method of deriving formulas for eigenfunctions concentrated in a neighborhood of a closed geodesic is proposed. It is based on the technique of ray expansions with a complex eikonal. The method used is closely related to the method of complex germ of V. P. Maslov.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972).
V. P. Maslov, The Complex WKB Method and Nonlinear Equations [in Russian], Moscow (1977).
V. E. Nomofilov, “Asymptotic solutions of a system of equations of second-order concentrated in a neighborhood of a ray,” this issue, p. 1854.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituts im. V. A. Steklova AN SSSR, Vol. 104, pp. 6–13, 1981.
Rights and permissions
About this article
Cite this article
Babich, V.M., Ulin, V.V. Complex ray solutions and eigenfunctions concentrated in a neighborhood of a closed geodesic. J Math Sci 20, 1749–1753 (1982). https://doi.org/10.1007/BF01119354
Issue Date:
DOI: https://doi.org/10.1007/BF01119354