Conservation laws and Calapso-Guichard deformations of equations describing pseudo-spherical surfaces (Q2737984)

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.