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

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

2002-12-19

arxiv.org/abs/nlin/0212045v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

31 pages

Scientific paper

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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