Advertisement

Edge Catastrophes in Diffraction Problems

  • A. S. KryukovskyEmail author
  • D. S. Lukin
ELECTRODYNAMICS AND WAVE PROPAGATION

Abstract—The application of the wave theory of edge catastrophes to the asymptotic solution of diffraction problems on bodies with curvilinear edges is considered. As an example, the diffraction of a converging scalar wave on a curvilinear ideally conducting screen in a homogeneous medium is studied, leading to the formation of C4 and K4, 2 edge catastrophes.

Notes

FUNDING

This study was financially supported by the Russian Foundation for Basic Research (project nos. 18-02-00544-a, 17-02-01183-a).

REFERENCES

  1. 1.
    R. B. Vaganov and B. Z. Katsenelenbaum, Fundamentals of the Diffraction Theory (Nauka, Moscow, 1982) [in Russian].zbMATHGoogle Scholar
  2. 2.
    T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, London, 1978; Mir, Moscow, 1980).Google Scholar
  3. 3.
    D. S. Lukin and E. A. Palkin, Numerical Canonical Method in Problems of Diffraction and Propagation of Electromagnetic Waves in Inhomogeneous Media (MFTI, Moscow, 1982) [in Russian].zbMATHGoogle Scholar
  4. 4.
    A. S. Kryukovskii and A. V. Orlov, J. Commun. Technol. Electron. 55, 270 (2010).CrossRefGoogle Scholar
  5. 5.
    A. S. Kryukovskii and Yu. V. Saren, J. Commun. Technol. Electron. 47, 55 (2002).Google Scholar
  6. 6.
    V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularity of Differentiable Manifolds, Part 1: Classification of Critical Points of Caustic Surfaces and Wavefronts (Nauka, Moscow, 1982) [in Russian].Google Scholar
  7. 7.
    A. S. Kryukovskii, D. S. Lukin, E. A. Palkin, and D. S. Rastyagaev, J. Commun. Technol. Electron. 51, 1155 (2006).CrossRefGoogle Scholar
  8. 8.
    A. S. Kryukovskii, D. S. Lukin, and D. V. Rastyagaev, Russian J. Math. Phys. 16, 232 (2009).CrossRefGoogle Scholar
  9. 9.
    A. S. Kryukovskii, Uniform Asymptotic Theory of Boundary and Angular Wave Catastrophes (Ros. Nov. Univ., Moscow, 2013) [in Russian].Google Scholar
  10. 10.
    A. S. Kryukovskii and D. S. Lukin, J. Commun. Technol. Electron. 43, 971 (1998).Google Scholar
  11. 11.
    A. S. Kryukovskii and D. S. Lukin, J. Commun. Technol. Electron. 48, 931 (2003).Google Scholar
  12. 12.
    A. S. Kryukovskii and D. S. Lukin, Radiotekh. Elektron. (Moscow) 26, 1121 (1981).Google Scholar
  13. 13.
    A. S. Kryukovskii, J. Commun. Technol. Electron. 41, 51 (1996).Google Scholar
  14. 14.
    S. L. Karepov and A. S. Kryukovskii, J. Commun. Technol. Electron. 46, 34 (2001).Google Scholar
  15. 15.
    A. S. Kryukovskii and D. S. Lukin, Edge and Angular Catastrophes in the Uniform Geometric Theory of Diffraction. Tutorial (MFTI, Moscow, 1999) [in Russian].Google Scholar
  16. 16.
    A. S. Kryukovskii, D. S. Lukin, E. A. Palkin, and D. V. Rastyagaev, in Proc. Workshop on Diffraction and Propagation of Waves, Moscow, Febr. 7–15,1993 (MFTI, Moscow, 1993), p. 36.Google Scholar
  17. 17.
    A. M. Balykina and A. S. Kryukovskii, J. Commun. Technol. Electron. 60, 497 (2015).Google Scholar
  18. 18.
    T. V. Dorokhina, A. S. Kryukovskii, and D. S. Lukin, Elektromagn. Volny i Elektron. Sist. 12 (8), 71 (2007).Google Scholar
  19. 19.
    T. Pearcey, Philos. Mag. 37, 311 (1964).MathSciNetCrossRefGoogle Scholar
  20. 20.
    E. B. Ipatov, A. S. Kryukovskii, D. S. Lukin, and D. V. Rastyagaev, Radiotekh. Elektron. (Moscow) 39, 538 (1994).Google Scholar
  21. 21.
    V. A. Borovikov and B. E. Kinber, Geometrical Diffraction Theory (Sovetskoe Radio, Moscow, 1970) [in Russian].zbMATHGoogle Scholar
  22. 22.
    V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of Diffraction of Short Waves (Nauka, Moscow, 1973) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Russian New UniversityMoscowRussia

Personalised recommendations