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On generalized Bäcklund transformations for equations describing pseudo-spherical surfaces

✍ Scribed by Enrique G. Reyes

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
222 KB
Volume
45
Category
Article
ISSN
0393-0440

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✦ Synopsis

It is shown that each one-parameter subgroup of SL(2, R) gives rise to a local correspondence theorem between suitably generic solutions of arbitrary scalar equations describing pseudo-spherical surfaces. Thus, if appropriate genericity conditions are satisfied, there exist local transformations between any two solutions of scalar equations arising as integrability conditions of sl(2, R)-valued linear problems.

A complete characterization of evolution equations u t = K(x, t, u, u x , . . . , u x k ) which are of strictly pseudo-spherical type is also provided.

📜 SIMILAR VOLUMES

On Differential Equations Describing Pse
On Differential Equations Describing Pseudo-Spherical Surfaces
✍ N. Kamran; K. Tenenblat 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 717 KB

We give a complete classification of the evolution equations \(\partial u / \partial t=\) \(F\left(u, \hat{c} u / \partial x, \ldots . \hat{\sigma}^{\star} u / \partial x^{k}\right)\) which describe pseudo-spherical surfaces, without any a priori assumptions on the presence of a spectral parameter.