High-frequency diffraction by a contour with a jump of curvature is addressed. The outgoing wavefield on the limit ray is studied in the framework of ray theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. F. Filippov, “Reflection of a wave from a boundary composed of arcs of variable curvature”, J. Appl. Math. Mech. (PMM), 34, No. 6, 1014–1023 (1970).
A. V. Popov, “Backscattering from a line of jump of curvature,” in: Proceedings of the 5th All-USSR Symposium on Diffraction and Wave Propagation, Nauka, Leningrad (1971), pp. 171–175.
L. Kaminetzky and J. B. Keller, “Diffraction coefficients for higher order edges and vertices,” SIAM J. Appl. Math., 22, No. 1, 109–134 (1972).
N. Y. Kirpichnikova and V. B. Philippov, “Diffraction of whispering gallery waves by a conjunction line,” J. Math. Sci., 96, No. 4, 3342–3350 (1999).
A. S. Kirpichnikova and V. B. Philippov, “Diffraction by a line of curvature jump (a special case),” IEEE Trans. Antennas Propagation, 49, No. 12, 1618–1623 (2001).
Z. M. Rogoff and A. P. Kiselev, “Diffraction at jump of curvature on an impedance boundary,” Wave Motion, 33, No. 2, 183–208 (2001).
E. A. Zlobina and A. P. Kiselev, “High-frequency diffraction by a contour with a jump of curvature,” in: Proceedings of the International Conference “Days on Diffraction (DD) 2018”, St. Petersburg (2018), pp. 325–328.
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Short-Wavelength Diffraction Theory, Alpha Science, Oxford (1972).
G. D. Malyuzhinets, “Developments in our concepts of diffraction phenomena (on the 130th anniversary of the death of Thomas Young),” Physics Uspekhi,69(2), No. 5, 749-–758 (1959).
I. G. Kondrat’ev and G. D. Malyuzhinets, “Diffraction of waves”, in: Physics Encyclopedia, Vol. 1, Sov. Entsiklopedia, Moscow (1988), pp. 664–667.
V. A. Borovikov and B. E. Kinber, Geometrical Theory of Diffraction, Institute of Electrical Engineers, London (1994).
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, Robert E. Krieger Publishing Company, Malabar (1981).
N. V. Tsepelev, “Some special solutions of the Helmholtz equation”, J. Sov. Math., 11, No. 3, 497—501 (1979).
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York (1953).
A. L. Brodskaya, A. V. Popov, and S. A. Khozioski, “Asymptotics of the wave refected by a cone in the penumbra region,” in: Proceedings of the 5th All-USSR Symposium on Diffraction and Wave Propagation, Nauka, Moscow-Yerevan (1973), pp. 223–231.
A. Popov, A. Ladyzhensky (Brodskaya), and S. Khozioski, “Uniform asymptotics of the wave diffracted by a cone of arbitrary cross section,” Russ. J. Math. Phys., 16, No. 2, 296–299 (2009).
I. M. Gelfand and G. E. Shilov, Generalized Functions: Properties and Operations, Academic Press, New York & London (1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 471, 2018, pp. 113–123.
Rights and permissions
About this article
Cite this article
Zlobina, E.A., Kiselev, A.P. High-Frequency Diffraction by a Contour with a Jump of Curvature: the Limit Ray. J Math Sci 243, 707–714 (2019). https://doi.org/10.1007/s10958-019-04572-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-019-04572-8