Conservation laws and Calapso-Guichard deformations of equations describing pseudo-spherical surfaces. (English) Zbl 0992.53005

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.


53A05 Surfaces in Euclidean and related spaces
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
35L65 Hyperbolic conservation laws
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI


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