The Degasperis-Procesi equation as a non-metric Euler equation
نویسندگان
چکیده
In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of b-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fréchet space of all smooth functions on the circle.
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ar X iv : 0 90 8 . 05 08 v 1 [ m at h - ph ] 4 A ug 2 00 9 THE DEGASPERIS - PROCESI EQUATION AS A NON - METRIC EULER EQUATION
In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of b-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Proces...
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