The Degasperis-Procesi equation as a non-metric Euler equation Escher, Joachim; Kolev, Boris

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Authors
Escher, Joachim ; Kolev, Boris
Appears In
Mathematische Zeitschrift
Subjects
mathematical physics; 35q53, 58d05; diffeomorphisms group of the circle
Audience
Academic
Summary
Byline: Joachim Escher (1), Boris Kolev (2) Keywords: Euler equation; Diffeomorphisms group of the circle; Degasperis--Procesi equation; 35Q53; 58D05 Abstract: In this paper we present a geometric interpretation of the Degasperis--Procesi (DP) 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 DP and the Camassa--Holm equation as an ODE on the Frechet space of all smooth functions on the circle. Author Affiliation: (1) Institute for Applied Mathematics, University of Hannover, 30167, Hannover, Germany (2) CMI, 39 rue F. Joliot-Curie, 13453, Marseille Cedex 13, France Article History: Registration Date: 15/09/2010 Received Date: 15/09/2009 Accepted Date: 11/09/2010 Online Date: 28/09/2010
Bookmark
http://trove.nla.gov.au/work/188611
Work ID
188611

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