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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 438, Pages 46–72 (Mi znsl6183)  
Evolution of wave field jumps near caustics (elementary approach)

M. I. Belishevab, A. F. Vakulenkoa, A. Ya. Kazakovcd

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
c St. Petersburg State University of Technology and Design, St. Petersburg, Russia
d St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
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Abstract: The Poisson formula solving a $3$-dim Cauchy problem for the wave equation is applied to study behavior of the wave field singularities (jumps) near caustics in the $2$-dim and $3$-dim cases. The approach of quite elementary character enables one to describe the focusing effects in detail.
Key words and phrases: time-domain wave fields, propagation of jumps, singularities near caustics.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00535А
Saint Petersburg State University 6.38.670.2013
Received: 12.10.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 1, Pages 27–46
DOI: https://doi.org/10.1007/s10958-017-3391-7
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. I. Belishev, A. F. Vakulenko, A. Ya. Kazakov, “Evolution of wave field jumps near caustics (elementary approach)”, Mathematical problems in the theory of wave propagation. Part 45, Zap. Nauchn. Sem. POMI, 438, POMI, St. Petersburg, 2015, 46–72; J. Math. Sci. (N. Y.), 224:1 (2017), 27–46
Citation in format AMSBIB
\Bibitem{BelVakKaz15}
\by M.~I.~Belishev, A.~F.~Vakulenko, A.~Ya.~Kazakov
\paper Evolution of wave field jumps near caustics (elementary approach)
\inbook Mathematical problems in the theory of wave propagation. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 438
\pages 46--72
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6183}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3501066}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 27--46
\crossref{https://doi.org/10.1007/s10958-017-3391-7}
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