The Soliton Content of the Camassa–Holm and Hunter–Saxton Equations
نویسندگان
چکیده
The notion of a scalar equation describing pseudo-spherical surfaces is reviewed. It is shown that if an equation admits this structure, the existence of conservation laws, symmetries, and quadratic pseudo-potentials, can be studied by geometrical means. As an application, it is pointed out that the important Camassa–Holm and Hunter–Saxton equations possess features considered to be characteristic of standard “soliton” equations: an infinite number of local conservation laws, “Miura transformations”, a zero curvature formulation, and nonlocal symmetries.
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