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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 090, 37 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.090 (Mi sigma767) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$

Mariya N. Kuznetsovaa, Asli Pekcanb, Anatoliy V. Zhiberc

a Ufa State Aviation Technical University, 12 K. Marx Str., Ufa, Russia
b Department of Mathematics, Istanbul University, Istanbul, Turkey
c Ufa Institute of Mathematics, Russian Academy of Science, 112 Chernyshevskii Str., Ufa, Russia
Full-text PDF (552 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2012.090
Abstract: We present the complete classification of equations of the form $u_{xy} = f(u, u_x, u_y)$ and the Klein–Gordon equations $v_{xy} = F(v)$ connected with one another by differential substitutions $v = \varphi(u, u_x, u_y)$ such that $\varphi_{u_x}\varphi_{u_y}\neq 0$ over the ring of complex-valued variables.
Keywords: Klein–Gordon equation; differential substitution.
Received: April 25, 2012; in final form November 14, 2012; Published online November 26, 2012
Bibliographic databases:
Document Type: Article
MSC: 35L70
Language: English
Citation: 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.
Citation in format AMSBIB
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\by Mariya~N.~Kuznetsova, Asli~Pekcan, Anatoliy~V.~Zhiber
\paper The Klein--Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$
\jour SIGMA
\yr 2012
\vol 8
\papernumber 090
\totalpages 37
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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