On Transformations of the Rabelo Equations

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.

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (4)

• The short pulse equation is integrable
• Solitary wave solutions of the short pulse equation
• The Bi-Hamiltonian Structure of the Short Pulse Equation
• The Calogero equation and Liouville type equations

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• On integrability of the vector short pulse equation
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• The new integrable deformations of short pulse equation and sine-Gordon equation, and their solutions
• On a Whitham-Type Equation
• On integrability of the Yao-Zeng two-component short-pulse equation
• Integrability of a generalized short pulse equation revisited
• On a new avatar of the sine-Gordon equation
• Modeling of Ultra-Short Soliton Propagation in Deterministic and Stochastic Nonlinear Cubic Media