Abstract

Zero curvature formulations, pseudo-potentials, modified versions, "Miura transformations", conservation laws, and nonlocal symmetries of the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations are investigated from a unified point of view: these three equations belong to a two-parameter family of equations describing pseudo-spherical surfaces, and therefore their basic integrability properties can be studied by geometrical means. © Birkhäuser Verlag Basel/Switzerland 2007.