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✦   LIBER   ✦

On formal integrability of evolution equations and local geometry of surfaces

✍ Scribed by Mikhail V. Foursov; Peter J. Olver; Enrique G. Reyes

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
102 KB
Volume
15
Category
Article
ISSN
0926-2245

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✦ Synopsis

Some relationships between local differential geometry of surfaces and integrability of evolutionary partial differential equations are studied. It is proven that every second order formally integrable equation describes pseudo-spherical surfaces. A classification of integrable equations of Boussinesq type is presented, and it is shown that they can be interpreted geometrically as "equations describing hyperbolic affine surfaces".

πŸ“œ SIMILAR VOLUMES

Pseudo-spherical Surfaces and Integrabil
Pseudo-spherical Surfaces and Integrability of Evolution Equations
✍ Enrique G. Reyes πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 446 KB

A complete classification of evolution equations u t =F(x, t, u, u x , ..., u x k ) which describe pseudo-spherical surfaces, is given, thus providing a systematic procedure to determine a one-parameter family of linear problems for which the given equation is the integrability condition. It is show