2011-12-01, English, Article, Report edition: The Degasperis--Procesi equation as a non-metric Euler equation.(Report) Escher, Joachim; Kolev, Boris

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Physical Description
  • Report
  • Magazine/​Journal article
Published
  • Springer, 2011 Dec
Language
  • English

Edition details

Title
  • The Degasperis--Procesi equation as a non-metric Euler equation.(Report)
Also Titled
  • The Degasperis--Procesi equation as a non-metric Euler equation.
Appears In
  • Mathematische Zeitschrift, v.269, no.3-4, 2011 Dec, p.1137(17) (ISSN: 0025-5874)
Author
  • Escher, Joachim
  • Kolev, Boris
Published
  • Springer, 2011 Dec
Physical Description
  • Report
  • Magazine/​Journal article
Subjects
Target 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
Terms of Use
  • COPYRIGHT 2011 Springer
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 273086909

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