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Geometric Integrability of the Camassa–Holm Equation

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Abstract

It is observed that the Camassa–Holm equation describes pseudo-spherical surfaces and that therefore, its integrability properties can be studied by geometrical means. An sl(2, R)-valued linear problem whose integrability condition is the Camassa–Holm equation is presented, a ‘Miura transform’ and a ‘modified Camassa–Holm equation’ are introduced, and conservation laws for the Camassa–Holm equation are then directly constructed. Finally, it is pointed out that this equation possesses a nonlocal symmetry, and its flow is explicitly computed.

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  1. Department of Mathematics, Yale University, PO Box 208283, New Haven, CT, 06520–8283, U.S.A.

    Enrique G. Reyes

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  1. Enrique G. Reyes
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Reyes, E.G. Geometric Integrability of the Camassa–Holm Equation. Letters in Mathematical Physics 59, 117–131 (2002). https://doi.org/10.1023/A:1014933316169

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