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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 393, Pages 167–177 (Mi znsl4622)  
This article is cited in 14 scientific papers (total in 14 papers)

Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution

A. P. Kiseleva, A. B. Plachenovb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow, Russia
Full-text PDF (245 kB) Citations (14)
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Abstract: A review of earlier generalizations of the classical Bateman solution, involving an arbitrary function, is presented. Its further generalization, described by $m(m-1)$ real parameters characterizing the phase, is given. Under a proper choice of the arbitrary function, it may describe Gaussian beam or Gaussian packet.
Key words and phrases: wave equation, exact solutijns, localized waves, Bateman solutions.
Received: 08.10.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 4, Pages 605–610
DOI: https://doi.org/10.1007/s10958-012-0944-7
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. P. Kiselev, A. B. Plachenov, “Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution”, Mathematical problems in the theory of wave propagation. Part 41, Zap. Nauchn. Sem. POMI, 393, POMI, St. Petersburg, 2011, 167–177; J. Math. Sci. (N. Y.), 185:4 (2012), 605–610
Citation in format AMSBIB
\Bibitem{KisPla11}
\by A.~P.~Kiselev, A.~B.~Plachenov
\paper Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution
\inbook Mathematical problems in the theory of wave propagation. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 393
\pages 167--177
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4622}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870211}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 185
\issue 4
\pages 605--610
\crossref{https://doi.org/10.1007/s10958-012-0944-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866540795}
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  • https://www.mathnet.ru/eng/znsl/v393/p167
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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