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Zap. Nauchn. Sem. POMI, 2015, Volume 438, Pages 73–82 (Mi znsl6184)  

This article is cited in 3 scientific papers (total in 3 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

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


Full text: PDF file (204 kB)
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English version:
Journal of Mathematical Sciences (New York), 2017, 224:1, 47–53

Bibliographic databases:

Document Type: Article
UDC: 517.95+530.1+535.24+537.8
Received: 12.11.2015

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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Blagoveshchensky A.S., Kiselev A.P., “A Relation Between the Sheppard-Saghafi Solution and a Certain Solution of the Wave Equation With a Singularity At a Running Point”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 67–68  crossref  isi  scopus
    2. A. S. Blagoveshchenskii, A. P. Kiselev, “A relation between two simple localized solutions of the wave equation”, Comput. Math. Math. Phys., 57:6 (2017), 953–955  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. S. Blagoveshchensky, A. M. Tagirdzhanov, A. P. Kiselev, “On the Bateman–Hörmander solution of the wave equation, having a singularity at a running point”, Matematicheskie voprosy teorii rasprostraneniya voln. 48, Posvyaschaetsya pamyati Aleksandra Pavlovicha KAChALOVA, Zap. nauchn. sem. POMI, 471, POMI, SPb., 2018, 76–85  mathnet
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