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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 1, Pages 148–168
DOI: https://doi.org/10.4213/tmf10421
(Mi tmf10421)
 

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

Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side

A. Yu. Anikin, A. I. Klevin

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (993 kB) Citations (1)
References:
Abstract: We construct the leading term of the semiclassical asymptotic solution of the Helmholtz equation with a small parameter in the localized right-hand side. This equation arises, for example, in the problem of ocean acoustics, in which the small parameter is given by the ratio of the characteristic scale of the “vertical” coordinate to that of the other coordinates. The equation is considered in the region bounded in the “vertical” coordinate; it is divided into two layers, with the coefficient in the Helmholtz equation and the derivative of the solution having fixed jump discontinuities at the interface. The technique for constructing the asymptotics involves the operator separation of variables (adiabatic approximation) and the use of the recently developed method for constructing asymptotics of equations with localized right-hand sides in the equations obtained after the variable separation.
Keywords: Helmholtz equation, equation with a right-hand side, semiclassical asymptotics, Maslov canonical operator.
Funding agency Grant number
Russian Science Foundation 21-11-00341
This work was supported by the Russian Science Foundation (grant No. 21-11-00341),
https://rscf.ru/en/project/21-11-00341/.
Received: 13.12.2022
Revised: 15.02.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 1, Pages 1036–1054
DOI: https://doi.org/10.1134/S0040577923070103
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Yu. Anikin, A. I. Klevin, “Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side”, TMF, 216:1 (2023), 148–168; Theoret. and Math. Phys., 216:1 (2023), 1036–1054
Citation in format AMSBIB
\Bibitem{AniKle23}
\by A.~Yu.~Anikin, A.~I.~Klevin
\paper Asymptotics of the~Helmholtz equation solutions in a~two-layer medium with a~localized right-hand side
\jour TMF
\yr 2023
\vol 216
\issue 1
\pages 148--168
\mathnet{http://mi.mathnet.ru/tmf10421}
\crossref{https://doi.org/10.4213/tmf10421}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4619872}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216.1036A}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 1
\pages 1036--1054
\crossref{https://doi.org/10.1134/S0040577923070103}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85165561345}
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  • https://www.mathnet.ru/eng/tmf10421
  • https://doi.org/10.4213/tmf10421
  • https://www.mathnet.ru/eng/tmf/v216/i1/p148
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:144
    Full-text PDF :12
    Russian version HTML:74
    References:22
    First page:12
     
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