
SIGMA 3 (2007), 086, 8 pages arXiv:0705.2889
http://dx.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 secondorder nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constantcharacteristic form we relate them to some wellstudied integrable equations. Two of the Rabelo equations are found to be related to the sineGordon 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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