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Evolution of Wave Field Jumps Near Caustics (Elementary Approach)

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The Poisson formula solving the 3-dim Cauchy problem for the wave equation is applied to the study of the behavior of wave field singularities (jumps) near caustics in the 2-dim and 3-dim cases. A quite elementary approach enables one to describe focusing effects in detail.

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Author information

Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg University, St. Petersburg, Russia

    M. I. Belishev

  2. St. Petersburg State University of Technology and Design, St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia

    A. Ya. Kazakov

  3. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    A. F. Vakulenko

Authors
  1. M. I. Belishev
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  2. A. Ya. Kazakov
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  3. A. F. Vakulenko
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Corresponding author

Correspondence to M. I. Belishev.

Additional information

Dedicated to the jubilee of Vasilii Mikhailovich Babich

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 438, 2015, pp. 46–72.

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Belishev, M.I., Kazakov, A.Y. & Vakulenko, A.F. Evolution of Wave Field Jumps Near Caustics (Elementary Approach). J Math Sci 224, 27–46 (2017). https://doi.org/10.1007/s10958-017-3391-7

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  • DOI: https://doi.org/10.1007/s10958-017-3391-7

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