On Transformations of the Rabelo Equations
Exactly Solvable and Integrable Systems
2008-04-24 v2 Mathematical Physics
Analysis of PDEs
Differential Geometry
math.MP
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.
Cite
@article{arxiv.0705.2889,
title = {On Transformations of the Rabelo Equations},
author = {Anton Sakovich and Sergei Sakovich},
journal= {arXiv preprint arXiv:0705.2889},
year = {2008}
}