Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1137-1153 |
| Seitenumfang | 17 |
| Fachzeitschrift | Mathematische Zeitschrift |
| Jahrgang | 269 |
| Ausgabenummer | 3-4 |
| Publikationsstatus | Veröffentlicht - 28 Sept. 2010 |
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 Fréchet space of all smooth functions on the circle.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Mathematische Zeitschrift, Jahrgang 269, Nr. 3-4, 28.09.2010, S. 1137-1153.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - The Degasperis-Procesi equation as a non-metric Euler equation
AU - Escher, Joachim
AU - Kolev, Boris
PY - 2010/9/28
Y1 - 2010/9/28
N2 - 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 Fréchet space of all smooth functions on the circle.
AB - 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 Fréchet space of all smooth functions on the circle.
KW - Degasperis-Procesi equation
KW - Diffeomorphisms group of the circle
KW - Euler equation
UR - http://www.scopus.com/inward/record.url?scp=81555201634&partnerID=8YFLogxK
U2 - 10.1007/s00209-010-0778-2
DO - 10.1007/s00209-010-0778-2
M3 - Article
AN - SCOPUS:81555201634
VL - 269
SP - 1137
EP - 1153
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -