Journal of Mathematical Sciences

, Volume 243, Issue 5, pp 707–714 | Cite as

High-Frequency Diffraction by a Contour with a Jump of Curvature: the Limit Ray

  • E. A. ZlobinaEmail author
  • A. P. Kiselev

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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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).CrossRefGoogle Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    L. Kaminetzky and J. B. Keller, “Diffraction coefficients for higher order edges and vertices,” SIAM J. Appl. Math., 22, No. 1, 109–134 (1972).MathSciNetCrossRefGoogle Scholar
  4. 4.
    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).MathSciNetCrossRefGoogle Scholar
  5. 5.
    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).MathSciNetCrossRefGoogle Scholar
  6. 6.
    Z. M. Rogoff and A. P. Kiselev, “Diffraction at jump of curvature on an impedance boundary,” Wave Motion, 33, No. 2, 183–208 (2001).CrossRefGoogle Scholar
  7. 7.
    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.Google Scholar
  8. 8.
    V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Short-Wavelength Diffraction Theory, Alpha Science, Oxford (1972).Google Scholar
  9. 9.
    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).MathSciNetCrossRefGoogle Scholar
  10. 10.
    I. G. Kondrat’ev and G. D. Malyuzhinets, “Diffraction of waves”, in: Physics Encyclopedia, Vol. 1, Sov. Entsiklopedia, Moscow (1988), pp. 664–667.Google Scholar
  11. 11.
    V. A. Borovikov and B. E. Kinber, Geometrical Theory of Diffraction, Institute of Electrical Engineers, London (1994).CrossRefGoogle Scholar
  12. 12.
    H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, Robert E. Krieger Publishing Company, Malabar (1981).zbMATHGoogle Scholar
  13. 13.
    N. V. Tsepelev, “Some special solutions of the Helmholtz equation”, J. Sov. Math., 11, No. 3, 497—501 (1979).CrossRefGoogle Scholar
  14. 14.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York (1953).zbMATHGoogle Scholar
  15. 15.
    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.Google Scholar
  16. 16.
    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).Google Scholar
  17. 17.
    I. M. Gelfand and G. E. Shilov, Generalized Functions: Properties and Operations, Academic Press, New York & London (1968).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Steklov Mathematical Institute, St. Petersburg DepartmentInstitute of Mechanical Engineering RASSt. PetersburgRussia

Personalised recommendations