Abstract
The propagation of whispering gallery waves near a concave (from the side of the wave field) boundary having a flat point is studied. As in [4], the problem that arises for an equation of Schrodinger type is solved by the method of grids. The results of the computations are presented as shadow figures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. A. Fock, Electromagnetic Diffraction and Propagation Problems, Pergamon (1965).
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Nauka, Moscow (1972).
M. M. Popov, “On the problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,62, 197–206 (1976).
M. M. Popov and I. Pshenchik, “Numerical solution of the problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,62, 207–219 (1976).
M. M. Popov, “Examples of exactly solvable scattering problems for the parabolic equation of diffraction theory,” J. Sov. Math.,22, No. 1 (1983).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 78, pp. 203–210, 1978.
Rights and permissions
About this article
Cite this article
Popov, M.M., Pshenchik, I. Whispering gallery waves in a neighborhood of a flat point of a concave boundary. J Math Sci 22, 1136–1142 (1983). https://doi.org/10.1007/BF01305296
Issue Date:
DOI: https://doi.org/10.1007/BF01305296