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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 438, Pages 73–82 (Mi znsl6184)  
This article is cited in 7 scientific papers (total in 7 papers)

Simple solutions of the wave equation, singular at a ranning point, based on the complexified Bateman solution

A. S. Blagovestchenskiia, A. P. Kiselevbca, A. M. Tagirdzhanova

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (204 kB) Citations (7)
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Abstract: We suggest simple solutions of the homogeneous wave equation with constant propagation speed having a power-like singularity in a moving spatial point. The construction is are based on the complexified Bateman-type solution. Example of such a solution showing exponential decay with distance from the singular point is presented.
Key words and phrases: wave equation, exact solutions, propagation of discontinuities.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00535
Received: 12.11.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 1, Pages 47–53
DOI: https://doi.org/10.1007/s10958-017-3392-6
Bibliographic databases:
Document Type: Article
UDC: 517.95+530.1+535.24+537.8
Language: Russian
Citation: A. S. Blagovestchenskii, A. P. Kiselev, A. M. Tagirdzhanov, “Simple solutions of the wave equation, singular at a ranning point, based on the complexified Bateman solution”, Mathematical problems in the theory of wave propagation. Part 45, Zap. Nauchn. Sem. POMI, 438, POMI, St. Petersburg, 2015, 73–82; J. Math. Sci. (N. Y.), 224:1 (2017), 47–53
Citation in format AMSBIB
\Bibitem{BlaKisTag15}
\by A.~S.~Blagovestchenskii, A.~P.~Kiselev, A.~M.~Tagirdzhanov
\paper Simple solutions of the wave equation, singular at a~ranning point, based on the complexified Bateman solution
\inbook Mathematical problems in the theory of wave propagation. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 438
\pages 73--82
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6184}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3501067}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 47--53
\crossref{https://doi.org/10.1007/s10958-017-3392-6}
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  • https://www.mathnet.ru/eng/znsl/v438/p73
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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