Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zapiski Nauchnykh Seminarov POMI, 2004, Volume 308, Pages 9–22 (Mi znsl825)  

This article is cited in 11 scientific papers (total in 12 papers)

On $PC$-ansatz

V. M. Babich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
References:
Abstract: The subject of the paper is detailed consideration of known from seventies ansatz:
$$ e^{\operatorname{i}kl(x)}[AD_p(\sqrt{k}e^{-\frac\pi4}m(x))+ k^{-\frac12}e^{\frac\pi4}BD_p^\prime(\sqrt{k}e^{-\frac\pi4}m(x))], $$
where $A$ and $B$ are series:
$$ A=\sum_{s=0}^\infty\frac{A_s(x)}{(\operatorname{i}k)^s};\quad B=\sum_{s=0}^\infty\frac{B_s(x)}{(\operatorname{i}k)^s}. $$
Here $D_p$ are parabolic cylinder functions. Analytical expressions in the first approximation for wave field in the penumbra of the wave reflected by impedance or transparent cone were obtained.
Received: 29.01.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 132, Issue 1, Pages 2–10
DOI: https://doi.org/10.1007/s10958-005-0470-y
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: V. M. Babich, “On $PC$-ansatz”, Mathematical problems in the theory of wave propagation. Part 33, Zap. Nauchn. Sem. POMI, 308, POMI, St. Petersburg, 2004, 9–22; J. Math. Sci. (N. Y.), 132:1 (2006), 2–10
Citation in format AMSBIB
\Bibitem{Bab04}
\by V.~M.~Babich
\paper On $PC$-ansatz
\inbook Mathematical problems in the theory of wave propagation. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 308
\pages 9--22
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl825}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2092609}
\zmath{https://zbmath.org/?q=an:1082.35048}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 132
\issue 1
\pages 2--10
\crossref{https://doi.org/10.1007/s10958-005-0470-y}
Linking options:
  • https://www.mathnet.ru/eng/znsl825
  • https://www.mathnet.ru/eng/znsl/v308/p9
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:379
    Full-text PDF :93
    References:91
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024