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Mat. Sb., 1992, Volume 183, Number 11, Pages 45–54 (Mi msb1088)  

This article is cited in 3 scientific papers (total in 3 papers)

Infinite-parameter families of solutions of nonlinear differential equations

S. V. Khabirov


Abstract: A Bäcklund transformation of a nonlinear equation and additional invariance of it under a contact transformation permit the construction of a family of solutions depending on an arbitrary number of parameters. Boundary value problems are solved by choosing the parameters and the initial solution.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 303–311

Bibliographic databases:

UDC: 517.958
MSC: Primary 58G37; Secondary 35C05, 35K40, 35A30
Received: 10.10.1991

Citation: S. V. Khabirov, “Infinite-parameter families of solutions of nonlinear differential equations”, Mat. Sb., 183:11 (1992), 45–54; Russian Acad. Sci. Sb. Math., 77:2 (1994), 303–311

Citation in format AMSBIB
\Bibitem{Kha92}
\by S.~V.~Khabirov
\paper Infinite-parameter families of solutions of nonlinear differential equations
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 11
\pages 45--54
\mathnet{http://mi.mathnet.ru/msb1088}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1208213}
\zmath{https://zbmath.org/?q=an:0803.58058}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..303K}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 303--311
\crossref{https://doi.org/10.1070/SM1994v077n02ABEH003442}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994NF83500004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Khabirov, “Extension of differential substitutions”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 415–426  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. N. Kuznetsova, “O nelineinykh giperbolicheskikh uravneniyakh, svyazannykh differentsialnymi podstanovkami s uravneniem Kleina–Gordona”, Ufimsk. matem. zhurn., 4:3 (2012), 86–103  mathnet  mathscinet
    3. Mariya N. Kuznetsova, Asli Pekcan, Anatoliy V. Zhiber, “The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$”, SIGMA, 8 (2012), 090, 37 pp.  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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