Diffraction of a plane wave by a circular impedance cone is studied. Surface waves propagating from the vertex of the cone are discussed. The excitation coefficient is computed with the help of the incomplete separation of variables in the problem. Bibliography: 14 titles.
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J.-M. L. Bernard, “Methode analytique et transformes fonctionnelles pour la diffraction d'ondes par une singularite conique equation integrale de noyau non oscillant pour le cas d'impedance constante,” rapport CEA-R-5764, Editions Dist-Saclay (1997).
J.-M. L. Bernard and M. A. Lyalinov, “Diffraction of acoustic waves by an impedance cone of an arbitrary cross-section,’” Wave Motion, 33, 155–181 (2001).
J.-M. L. Bernard and M. A. Lyalinov, “Electromagnetic scattering by a smooth convex impedance one,” IMA Journ. Appl. Math., 33, 285–333 (2004).
M. A. Lyalinov, “Diffraction of a plane wave by an impedance one,” J. Math. Sciences, 127, No. 6, 2446–246 (2005).
M. A. Lyalinov, N. Y. Zhu, and V. P. Smyshlyaev, “Scattering of a plane electromagnetic wave by a circular hollow one with thin semi-transparent walls,” accepted in IMA J. Appl. Math. (2009).
J.-M. L. Bernard, M. A. Lyalinov, and N. Y. Zhu, “Analytical-numerical calculation of diffraction coefficients for a circular impedance one,” IEEE Trans. Antennas Propag., 56 (6), 1616–1623 (2008).
M. A. Lyalinov, “The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance one,” Russian J. Math. Physics, 16, No. 2, 277–286 (2009).
V. A. Borovikov, Diffraction by Polygons and Polytops [in Russian], Nauka, Moscow (1966).
V. P. Smyshlyaev, “Diffraction by conical surfaces at high frequences,” Wave Motion, 22, 311–324 (1995).
V. M. Babich, D. B. Dement'ev, B. A. Samokish, and V. P. Smyshlyaev, “One valuation of diffraction coefficients for arbitrary “non-singular” directions of a smooth convex one,” SIAM Appl. Math., 60 (2), 536–573 (2000).
D. S. Jones, “Scattering by a one,” Quaterly J. Mech. Appl. Math., 50, 499–523 (1997).
V. M. Babich and A. V. Kuznetsov, “On propagation of surface electromagnetic waves, analogous to the Rayleigh wave, in the case of Leontovich boundary conditions,” Zap. Nauchn. Semin. POMI, 324 (5), 5–19 (2005).
R. Grimshow, “Propagation of surface waves at high frequences,” J. Inst. Maths. Applics., 4, 174–193 (1968).
V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, Space-Time Ray Method [in Russian], Leningrad Univ., Leningrad (1985).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 369, 2009, pp. 95–109.
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Lyalinov, M.A. Diffraction of a plane acoustic wave on an impedance cone. Surface waves. J Math Sci 167, 651–659 (2010). https://doi.org/10.1007/s10958-010-9951-8
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DOI: https://doi.org/10.1007/s10958-010-9951-8