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Zbl 1136.35094
Sakovich, Anton; Sakovich, Sergei
On transformations of the Rabelo equations. (English)
[J] SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 086, 8 pp., electronic only (2007). ISSN 1815-0659/e

Summary: 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. By reducing the Rabelo equations to known ones their general solutions are obtained.

MSC 2000:: *35Q58 Other completely integrable PDE
35Q53 KdV-like equations
35C05 Solutions of PDE in closed form

Keywords: nonlinear Rabelo equations; sine-Gordon equation; Liouville equation; general solutions; transformations

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Zentralblatt MATH Berlin [Germany]