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Zap. Nauchn. Sem. POMI, 2014, Volume 422, Pages 131–149 (Mi znsl5766)  

This article is cited in 1 scientific paper (total in 1 paper)

Time-harmonic “complex source” wavefields and their sources in real space

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

a St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The paper concerns the complexified Green function of the 3D Helmholtz equation in the free space, which is interesting as an exact solution demonstrating Gaussian-beam behavior. This function involves a square root and satisfies an inhomogeneous Helmholtz equation, the right-hand side of which depends on the cut and on the branch of the root. We deal with the explicit description of this generalized function.

Key words and phrases: complex source, exact solutions, localized waves, Gaussian beams, Helmholtz equation.

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English version:
Journal of Mathematical Sciences (New York), 2015, 206:3, 315–327

UDC: 517.95+530.1+534.1+535.24+537.8+535.24
Received: 13.01.2014

Citation: A. M. Tagirdzhanov, A. S. Blagovestchenskii, A. P. Kiselev, “Time-harmonic “complex source” wavefields and their sources in real space”, Mathematical problems in the theory of wave propagation. Part 43, Zap. Nauchn. Sem. POMI, 422, POMI, St. Petersburg, 2014, 131–149; J. Math. Sci. (N. Y.), 206:3 (2015), 315–327

Citation in format AMSBIB
\Bibitem{TagBlaKis14}
\by A.~M.~Tagirdzhanov, A.~S.~Blagovestchenskii, A.~P.~Kiselev
\paper Time-harmonic ``complex source'' wavefields and their sources in real space
\inbook Mathematical problems in the theory of wave propagation. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 422
\pages 131--149
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5766}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 206
\issue 3
\pages 315--327
\crossref{https://doi.org/10.1007/s10958-015-2313-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940105525}


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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. A. M. Tagirdzhanov, A. P. Kiselev, “Gaussian wave packet based on the “complex source””, J. Math. Sci. (N. Y.), 214:3 (2016), 372–381  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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