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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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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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This publication is cited in the following articles:
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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.
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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
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V. M. Zhuravlev, “Multidimensional nonlinear Klein–Gordon equations and rivertons”, Theoret. and Math. Phys., 197:3 (2018), 1701–1713
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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
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