|
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
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
Citation:
Anton Sakovich, Sergei Sakovich, “On Transformations of the Rabelo Equations”, SIGMA, 3 (2007), 086, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma212 https://www.mathnet.ru/eng/sigma/v3/p86
|
Statistics & downloads: |
Abstract page: | 332 | Full-text PDF : | 76 | References: | 44 |
|