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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2005, Volume 46, Issue 6, Pages 26–35 (Mi pmtf2316)  
This article is cited in 8 scientific papers (total in 8 papers)

Invariant and partially invariant solutions of the Green–Naghdi equations

Yu. Yu. Bagderinaa, A. P. Chupakhinb

a Institute of Mathematics, Ural Scientific Center, Russian Academy of Sciences, Ufa, 450077, Russia
b Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Full-text PDF (221 kB) Citations (8)
Abstract: All invariant and partially invariant solutions of the Green–Naghdi equations are obtained that describe the second approximation of shallow water theory. It is proved that all nontrivial invariant solutions belong to one of the following types: Galilean-invariant, stationary, and self-similar solutions. The Galilean-invariant solutions are described by the solutions of the second Painleve equation, the stationary solutions by elliptic functions, and the self-similar solutions by the solutions of the system of ordinary differential equations of the fourth order. It is shown that all partially invariant solutions reduce to invariant solutions.
Keywords: Green–Naghdi equations, invariant and partially invariant solutions, Painleve equation.
Received: 27.01.2005
English version:
Journal of Applied Mechanics and Technical Physics, 2005, Volume 46, Issue 6, Pages 791–799
DOI: https://doi.org/10.1007/s10808-005-0136-z
Bibliographic databases:
Document Type: Article
UDC: 517.9; 532.592
Language: Russian
Citation: Yu. Yu. Bagderina, A. P. Chupakhin, “Invariant and partially invariant solutions of the Green–Naghdi equations”, Prikl. Mekh. Tekh. Fiz., 46:6 (2005), 26–35; J. Appl. Mech. Tech. Phys., 46:6 (2005), 791–799
Citation in format AMSBIB
\Bibitem{BagChu05}
\by Yu.~Yu.~Bagderina, A.~P.~Chupakhin
\paper Invariant and partially invariant solutions of the Green--Naghdi equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2005
\vol 46
\issue 6
\pages 26--35
\mathnet{http://mi.mathnet.ru/pmtf2316}
\elib{https://elibrary.ru/item.asp?id=15175980}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2005
\vol 46
\issue 6
\pages 791--799
\crossref{https://doi.org/10.1007/s10808-005-0136-z}
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  • https://www.mathnet.ru/eng/pmtf/v46/i6/p26
    • This publication is cited in the following 8 articles:
    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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