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Zbl 0992.53005
Reyes, Enrique G.
Conservation laws and Calapso-Guichard deformations of equations describing pseudo-spherical surfaces. (English)
[J] J. Math. Phys. 41, No.5, 2968-2989 (2000). ISSN 0022-2488; ISSN 1089-7658/e

From author's abstract: The relation between the Chern and Tenenblat approach to conservation laws of equations describing pseudo-spherical surfaces (conservation laws obtained from pseudo-spherical structure) and the more familiar ``Riccati equation" approach (conservation laws obtained from associated linear problem) is investigated. Two examples (cylindrical Korteweg-de Vries (KdV) and Lund-Regge equations) are presented. Chern and Tenenblat's point of view is then connected with the theory of soliton surfaces. A generalization of the original Chern-Tenenblat construction of conservation law-results and a reasonable family of large deformations for scalar equations describing pseudo-spherical surfaces, the ``equations describing Calapso-Guichard surfaces'', can be introduced. It is shown that these equations are also the integrability conditions of linear problems.
[Raul Ibáñez (Bilbao)]

MSC 2000:: *53A05 Surfaces in Euclidean space
37K25 Relations with differential geometry
35L65 Conservation laws
37K40 Soliton theory, asymptotic behavior of solutions
35Q53 KdV-like equations

Keywords: conservation laws; Riccati equation; pseudo-spherical surfaces; soliton surfaces

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Zentralblatt MATH Berlin [Germany]