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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2022, Volume 63, Issue 6, Pages 68–81
DOI: https://doi.org/10.15372/PMTF20220608 (Mi pmtf230) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Group classification of two-dimensional Green–Naghdi equations in the case of time-independent bottom topography

S. V. Meleshkoa, P. Siriwatb

a Institute of Science, Suranaree University of Technology, 30000, Nakhon Ratchasima, Thailand
b School of Science, Mae Fah Luang University, 57100, Chiang Rai, Thailand
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DOI: https://doi.org/10.15372/PMTF20220608
Abstract: The two-dimensional Green–Naghdi equations are investigated in the case of an uneven bottom topography. The function which determines the topography of the bottom and may depend on time is considered. A group classification of the equations under study with respect to the function describing the bottom topography is carried out using an algebraic approach.
Keywords: group classification, equivalence group, admissible Lee group, Green–Naghdi equations.
Funding agency Grant number
Russian Science Foundation 18-11-00238
Received: 14.03.2022
Revised: 21.04.2022
Accepted: 25.04.2022
English version:
Journal of Applied Mechanics and Technical Physics, 2022, Volume 63, Issue 6, Pages 972–983
DOI: https://doi.org/10.1134/S0021894422060086
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. V. Meleshko, P. Siriwat, “Group classification of two-dimensional Green–Naghdi equations in the case of time-independent bottom topography”, Prikl. Mekh. Tekh. Fiz., 63:6 (2022), 68–81; J. Appl. Mech. Tech. Phys., 63:6 (2022), 972–983
Citation in format AMSBIB
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\by S.~V.~Meleshko, P.~Siriwat
\paper Group classification of two-dimensional Green--Naghdi equations in the case of time-independent bottom topography
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2022
\vol 63
\issue 6
\pages 68--81
\mathnet{http://mi.mathnet.ru/pmtf230}
\crossref{https://doi.org/10.15372/PMTF20220608}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4560671}
\elib{https://elibrary.ru/item.asp?id=49930290}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2022
\vol 63
\issue 6
\pages 972--983
\crossref{https://doi.org/10.1134/S0021894422060086}
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  • https://www.mathnet.ru/eng/pmtf230
  • https://www.mathnet.ru/eng/pmtf/v63/i6/p68
    • This publication is cited in the following 1 articles:
    1. Yu A. Chirkunov, M. Yu Chirkunov, “New nonlinear models of dynamic longitudinal deformation of a viscoelastic rod”, International Journal of Non-Linear Mechanics, 160 (2024), 104654  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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    References:36
    First page:18
     
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