Pseudospherical surfaces and evolution equations. (English) Zbl 0605.35080

Chern, S. S.; Tenenblat, K.

Stud. Appl. Math. 74, 55-83 (1986).

The authors obtain a systematic procedure to determine the 1-forms for some nonlinear evolution equations (including KdV, MKdV, Sine-Gordon, Sinh-Gordon, Burgers equations, etc.), which describe pseudospherical surfaces. By using the geometric properties of a p.s.s., the Bäcklund transformations and conservation laws are obtained for some evolution equations. For any given nonlinear evolution equations (one doesn’t know whether they do or do not describe pseudospherical surfaces), it is still an important and interesting problem how to provide analytic information for such equations from geometrical properties.

Reviewer: Boling Guo

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
35A30	Geometric theory, characteristics, transformations in context of PDEs

Keywords:

nonlinear evolution equations; pseudospherical surfaces

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