Skip to main content
Log in

Edge Catastrophes in Diffraction Problems

  • ELECTRODYNAMICS AND WAVE PROPAGATION
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. R. B. Vaganov and B. Z. Katsenelenbaum, Fundamentals of the Diffraction Theory (Nauka, Moscow, 1982) [in Russian].

    MATH  Google Scholar 

  2. T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, London, 1978; Mir, Moscow, 1980).

  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].

    MATH  Google Scholar 

  4. A. S. Kryukovskii and A. V. Orlov, J. Commun. Technol. Electron. 55, 270 (2010).

    Article  Google Scholar 

  5. A. S. Kryukovskii and Yu. V. Saren, J. Commun. Technol. Electron. 47, 55 (2002).

    Google Scholar 

  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].

  7. A. S. Kryukovskii, D. S. Lukin, E. A. Palkin, and D. S. Rastyagaev, J. Commun. Technol. Electron. 51, 1155 (2006).

    Article  Google Scholar 

  8. A. S. Kryukovskii, D. S. Lukin, and D. V. Rastyagaev, Russian J. Math. Phys. 16, 232 (2009).

    Article  Google Scholar 

  9. A. S. Kryukovskii, Uniform Asymptotic Theory of Boundary and Angular Wave Catastrophes (Ros. Nov. Univ., Moscow, 2013) [in Russian].

    Google Scholar 

  10. A. S. Kryukovskii and D. S. Lukin, J. Commun. Technol. Electron. 43, 971 (1998).

    Google Scholar 

  11. A. S. Kryukovskii and D. S. Lukin, J. Commun. Technol. Electron. 48, 931 (2003).

    Google Scholar 

  12. A. S. Kryukovskii and D. S. Lukin, Radiotekh. Elektron. (Moscow) 26, 1121 (1981).

    Google Scholar 

  13. A. S. Kryukovskii, J. Commun. Technol. Electron. 41, 51 (1996).

    Google Scholar 

  14. S. L. Karepov and A. S. Kryukovskii, J. Commun. Technol. Electron. 46, 34 (2001).

    Google Scholar 

  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. 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.

  17. A. M. Balykina and A. S. Kryukovskii, J. Commun. Technol. Electron. 60, 497 (2015).

    Google Scholar 

  18. T. V. Dorokhina, A. S. Kryukovskii, and D. S. Lukin, Elektromagn. Volny i Elektron. Sist. 12 (8), 71 (2007).

    Google Scholar 

  19. T. Pearcey, Philos. Mag. 37, 311 (1964).

    Article  MathSciNet  Google Scholar 

  20. E. B. Ipatov, A. S. Kryukovskii, D. S. Lukin, and D. V. Rastyagaev, Radiotekh. Elektron. (Moscow) 39, 538 (1994).

    Google Scholar 

  21. V. A. Borovikov and B. E. Kinber, Geometrical Diffraction Theory (Sovetskoe Radio, Moscow, 1970) [in Russian].

    MATH  Google Scholar 

  22. V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of Diffraction of Short Waves (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

Download references

Funding

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. S. Kryukovsky.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kryukovsky, A.S., Lukin, D.S. Edge Catastrophes in Diffraction Problems. J. Commun. Technol. Electron. 64, 1224–1229 (2019). https://doi.org/10.1134/S1064226919110160

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226919110160

Navigation