Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 086, 8 pages      arXiv:0705.2889      https://doi.org/10.3842/SIGMA.2007.086
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

On Transformations of the Rabelo Equations

Anton Sakovich a and Sergei Sakovich b
a) National Centre of Particle and High Energy Physics, 220040 Minsk, Belarus
b) Institute of Physics, National Academy of Sciences, 220072 Minsk, Belarus

Received May 28, 2007, in final form August 22, 2007; Published online September 03, 2007

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.

Key words: nonlinear PDEs; transformations; integrability.

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