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Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations

Enrique G. Reyes
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Abstract

Zero curvature formulations, pseudo-potentials, modified versions, ``Miura transformations'', and nonlocal symmetries of the Korteweg--de Vries, Camassa-- Holm and Hunter--Saxton equations are investigated from an unified point of view: these three equations belong to a two--parameters family of equations ``describing pseudo-spherical surfaces'', and therefore their basic integrability properties can be studied by geometrical means.

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Enrique G. Reyes. 2002-12-19. Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations. https://arxiv.org/abs/nlin/0212045

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