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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 3, Pages 86–103 (Mi ufa157)  

This article is cited in 4 scientific papers (total in 4 papers)

On nonlinear hyperbolic differential equations related to the Klein–Gordon equation by differential substitutions

M. N. Kuznetsova

Ufa State Aviation Technical University, Ufa, Russia

Abstract: We present a complete classification of nonlinear hyperbolic differential equations in two independent variables $u_{xy}=f(u,u_x,u_y)$ reduced to the Klein–Gordon equation $v_{xy}=F(v)$ by differential substitutions of the special form $v=\varphi(u,u_x)$.

Keywords: nonlinear hyperbolic equations, differential substitutions, the Klein–Gordon equation.

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Bibliographic databases:
UDC: 517.95
Received: 26.03.2012

Citation: M. N. Kuznetsova, “On nonlinear hyperbolic differential equations related to the Klein–Gordon equation by differential substitutions”, Ufimsk. Mat. Zh., 4:3 (2012), 86–103

Citation in format AMSBIB
\Bibitem{Kuz12}
\by M.~N.~Kuznetsova
\paper On nonlinear hyperbolic differential equations related to the Klein--Gordon equation by differential substitutions
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 3
\pages 86--103
\mathnet{http://mi.mathnet.ru/ufa157}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429921}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. I. V. Rakhmelevich, “O dvumernykh giperbolicheskikh uravneniyakh so stepennoi nelineinostyu po proizvodnym”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2015, no. 1(33), 12–19  mathnet  crossref  elib
    3. V. M. Zhuravlev, “Multidimensional nonlinear Klein–Gordon equations and rivertons”, Theoret. and Math. Phys., 197:3 (2018), 1701–1713  mathnet  crossref  crossref  adsnasa  isi  elib
    4. S. Ya. Startsev, “Zakony sokhraneniya dlya giperbolicheskikh uravnenii: lokalnyi algoritm poiska proobraza otnositelno polnoi proizvodnoi”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 85–92  mathnet
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