Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
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


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2025, Volume 65, Number 4, Pages 446–459
DOI: https://doi.org/10.31857/S0044466925040041 (Mi zvmmf11952) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

The Jacobi–Maupertuis principle and Fermat variational principle in the problem of short-wave asymptotics in the solution of the Helmholtz equation with a localized source

S. Yu. Dobrokhotovab, I. A. Nosikova, A. A. Tolchennikovb

a Center for Integrable Systems, P.G. Demidov Yaroslavl State University, 150003, Yaroslavl, Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466925040041
Abstract: The problem of short-wave asymptotics of the Helmholtz equation with a localized right-hand side in the form of a rapidly decreasing function is considered in the article. We present an algorithm for calculating rays using the variational method and the wave field applying the canonical Maslov operator method for given boundary conditions. This approach is used for model examples, including those with a logarithmic feature of the ray family. In addition, we consider applications of the variational method for calculating rays in the illuminated region and in the caustic shadow region.
Key words: rays, wave field, Jacobi–Maupertuis principle, Fermat principle, canonical Maslov operator, functional.
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was supported by the Russian Science Foundation, grant no. 21-71-30011.
Received: 10.12.2024
Revised: 20.12.2024
Accepted: 04.02.2025
English version:
Computational Mathematics and Mathematical Physics, 2025, Volume 65, Issue 4, Pages 739–753
DOI: https://doi.org/10.1134/S0965542525700010
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: S. Yu. Dobrokhotov, I. A. Nosikov, A. A. Tolchennikov, “The Jacobi–Maupertuis principle and Fermat variational principle in the problem of short-wave asymptotics in the solution of the Helmholtz equation with a localized source”, Zh. Vychisl. Mat. Mat. Fiz., 65:4 (2025), 446–459; Comput. Math. Math. Phys., 65:4 (2025), 739–753
Citation in format AMSBIB
\Bibitem{DobNosTol25}
\by S.~Yu.~Dobrokhotov, I.~A.~Nosikov, A.~A.~Tolchennikov
\paper The Jacobi--Maupertuis principle and Fermat variational principle in the problem of short-wave asymptotics in the solution of the Helmholtz equation with a localized source
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2025
\vol 65
\issue 4
\pages 446--459
\mathnet{http://mi.mathnet.ru/zvmmf11952}
\elib{https://elibrary.ru/item.asp?id=82358152}
\transl
\jour Comput. Math. Math. Phys.
\yr 2025
\vol 65
\issue 4
\pages 739--753
\crossref{https://doi.org/10.1134/S0965542525700010}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11952
  • https://www.mathnet.ru/eng/zvmmf/v65/i4/p446
    • 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
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025