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.
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Reyes, E.G. Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations. Sel. math., New ser. 12, 241 (2006). https://doi.org/10.1007/s00029-006-0024-2
DOI: https://doi.org/10.1007/s00029-006-0024-2