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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2004, Volume 45, Issue 2, Pages 11–21 (Mi pmtf2353)  
This article is cited in 28 scientific papers (total in 28 papers)

Invariants of hyperbolic equations: solution of the Laplace problem

N. H. Ibragimov

Blekinge Institute of Technology, Karlskruna, 37179, Sweden
Full-text PDF (222 kB) Citations (28)
Abstract: This paper gives a solution of the Laplace problem, which consists of finding all invariants of the hyperbolic equations and constructing a basis of the invariants. Three new invariants of the first and second orders are found, and invariant-differentiation operators are constructed. It is shown that the new invariants, together with the two invariants detected by Ovsyannikov, form a basis such that any invariant of any order is a function of the basis invariants and their invariant derivatives.
Keywords: Laplace invariants, integration of hyperbolic equations, equivalence transformations, semi-invariants.
Received: 24.10.2003
English version:
Journal of Applied Mechanics and Technical Physics, 2004, Volume 45, Issue 2, Pages 158–166
DOI: https://doi.org/10.1023/B:JAMT.0000017577.36177.a2
Bibliographic databases:
Document Type: Article
UDC: 517.91
Language: Russian
Citation: N. H. Ibragimov, “Invariants of hyperbolic equations: solution of the Laplace problem”, Prikl. Mekh. Tekh. Fiz., 45:2 (2004), 11–21; J. Appl. Mech. Tech. Phys., 45:2 (2004), 158–166
Citation in format AMSBIB
\Bibitem{Ibr04}
\by N.~H.~Ibragimov
\paper Invariants of hyperbolic equations: solution of the Laplace problem
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2004
\vol 45
\issue 2
\pages 11--21
\mathnet{http://mi.mathnet.ru/pmtf2353}
\elib{https://elibrary.ru/item.asp?id=17249151}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2004
\vol 45
\issue 2
\pages 158--166
\crossref{https://doi.org/10.1023/B:JAMT.0000017577.36177.a2}
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  • https://www.mathnet.ru/eng/pmtf/v45/i2/p11
    • This publication is cited in the following 28 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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