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On Differential Equations Describing Pseudo-Spherical Surfaces

✍ Scribed by N. Kamran; K. Tenenblat

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
717 KB
Volume
115
Category
Article
ISSN
0022-0396

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✦ Synopsis

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. We also prove a local existence theorem to the effect that given two differential equations describing pseudo-spherical surfaces (not necessarily evolutionary), there exists, under a technical assumption, a smooth mapping transforming any suitably generic solution of one equation into a solution of the other. 1995 Academic Press. Inc.

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