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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 297, Pages 116–135 (Mi znsl1218)  
Combined method of calculation of the field of the point source in a wave guide

N. Ya. Kirpichnikovaa, V. B. Philippovb, N. G. Vlasjukb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Saint-Petersburg State University
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Abstract: The two-dimensional problem of propagation of waves, raised by a point source, in an interior wave guide is investigated. The Dirichlet (Neumann) boundary condition is given on the upper (lower) bound of the wave guide. The possibility of representation of the exact solution as a sum of the geometro-optical waves, the normal waves and the residual is shown. The sufficient conditions on the general amount of the detached normal and geometro-optical waves are obtained. The residual is expressed by the simple formula.
Received: 14.02.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 127, Issue 6, Pages 2402–2412
DOI: https://doi.org/10.1007/s10958-005-0189-9
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: N. Ya. Kirpichnikova, V. B. Philippov, N. G. Vlasjuk, “Combined method of calculation of the field of the point source in a wave guide”, Mathematical problems in the theory of wave propagation. Part 32, Zap. Nauchn. Sem. POMI, 297, POMI, St. Petersburg, 2003, 116–135; J. Math. Sci. (N. Y.), 127:6 (2005), 2402–2412
Citation in format AMSBIB
\Bibitem{KirPhiVla03}
\by N.~Ya.~Kirpichnikova, V.~B.~Philippov, N.~G.~Vlasjuk
\paper Combined method of calculation of the field of the point source in a~wave guide
\inbook Mathematical problems in the theory of wave propagation. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 297
\pages 116--135
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1218}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1981391}
\zmath{https://zbmath.org/?q=an:1116.78009}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 127
\issue 6
\pages 2402--2412
\crossref{https://doi.org/10.1007/s10958-005-0189-9}
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  • https://www.mathnet.ru/eng/znsl/v297/p116
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