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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 086, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.086 (Mi sigma212) 		 
This article is cited in 34 scientific papers (total in 34 papers)

On Transformations of the Rabelo Equations

Anton Sakovicha, Sergei Sakovichb

a National Centre of Particle and High Energy Physics, 220040 Minsk, Belarus
b Institute of Physics, National Academy of Sciences, 220072 Minsk, Belarus
Full-text PDF (188 kB) Citations (34)
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DOI: https://doi.org/10.3842/SIGMA.2007.086
Abstract: We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, and in this way their general solutions are obtained.
Keywords: nonlinear PDEs; transformations; integrability.
Received: May 28, 2007; in final form August 22, 2007; Published online September 3, 2007
Bibliographic databases:
Document Type: Article
MSC: 35Q58; 35Q53; 35C05
Language: English
Citation: Anton Sakovich, Sergei Sakovich, “On Transformations of the Rabelo Equations”, SIGMA, 3 (2007), 086, 8 pp.
Citation in format AMSBIB
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\by Anton Sakovich, Sergei Sakovich
\paper On Transformations of the Rabelo Equations
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\vol 3
\papernumber 086
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    		Symmetry, Integrability and Geometry: Methods and Applications
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