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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 23–33 (Mi znsl6029)  
This article is cited in 7 scientific papers (total in 7 papers)

Plane waves, Batmen's solutions and sources at infinity

A. S. Blagovestchensky

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (177 kB) Citations (7)
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Abstract: For threedimensional wave equation two equivalent statements are proved:
1) plane waves are not generated by a source at infinity,
2) Bateman's solution (the solution that obtained by the application of Kelvin–Bateman transformation to a plane wave) is the solution to wave equation everywhere in $\mathbb R^4$.
Key words and phrases: wave equation, plane wave, Kelvin–Bateman transformation, Bateman's solution, sources at infinity.
Received: 01.10.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 260–267
DOI: https://doi.org/10.1007/s10958-016-2775-4
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
Citation: A. S. Blagovestchensky, “Plane waves, Batmen's solutions and sources at infinity”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 23–33; J. Math. Sci. (N. Y.), 214:3 (2016), 260–267
Citation in format AMSBIB
\Bibitem{Bla14}
\by A.~S.~Blagovestchensky
\paper Plane waves, Batmen's solutions and sources at infinity
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 23--33
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485303}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 260--267
\crossref{https://doi.org/10.1007/s10958-016-2775-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960340541}
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  • https://www.mathnet.ru/eng/znsl/v426/p23
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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