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

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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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  1. Enrique G. Reyes

    Present address: Departamento de Matemáticas y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile

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  1. Department of Mathematics, University of Oklahoma, Norman, OK, 73019, U.S.A

    Enrique G. Reyes

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  1. Enrique G. Reyes
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Correspondence to Enrique G. Reyes.

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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

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  • DOI: https://doi.org/10.1007/s00029-006-0024-2

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