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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 218, Number 1, Pages 23–47
DOI: https://doi.org/10.4213/tmf10553
(Mi tmf10553)
 

This article is cited in 2 scientific papers (total in 2 papers)

Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side

I. A. Bogaevskyab, S. Yu. Dobrokhotovc, A. A. Tolchennikovc

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Research Institute for System Studies, Russian Academy of Sciences, Moscow, Russia
c Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
References:
Abstract: A model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit absorption principle, a Lagrangian surface naturally appears that has a logarithmic singularity at one point. Because of this singularity, the solution is localized not only in a neighborhood of the projection of the Lagrangian surface onto the coordinate space but also in a neighborhood of a certain ray “escaping” from the Lagrangian surface and going into the region forbidden in the classical approximation.
Keywords: semiclassical asymptotics, canonical Maslov operator, Lagrangian surfaces.
Funding agency Grant number
Russian Science Foundation 21-11-00341
This work is supported by the Russian Science Foundation (grant No. 21-11-00341).
Received: 01.06.2023
Revised: 01.06.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 218, Issue 1, Pages 19–40
DOI: https://doi.org/10.1134/S0040577924010021
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Bogaevsky, S. Yu. Dobrokhotov, A. A. Tolchennikov, “Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side”, TMF, 218:1 (2024), 23–47; Theoret. and Math. Phys., 218:1 (2024), 19–40
Citation in format AMSBIB
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\by I.~A.~Bogaevsky, S.~Yu.~Dobrokhotov, A.~A.~Tolchennikov
\paper Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side
\jour TMF
\yr 2024
\vol 218
\issue 1
\pages 23--47
\mathnet{http://mi.mathnet.ru/tmf10553}
\crossref{https://doi.org/10.4213/tmf10553}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4700041}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...218...19B}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 218
\issue 1
\pages 19--40
\crossref{https://doi.org/10.1134/S0040577924010021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85179156051}
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  • https://doi.org/10.4213/tmf10553
  • https://www.mathnet.ru/eng/tmf/v218/i1/p23
  • This publication is cited in the following 2 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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    References:22
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