Details
| Original language | English |
|---|---|
| Pages (from-to) | 313-322 |
| Number of pages | 10 |
| Journal | Journal of Geometric Mechanics |
| Volume | 3 |
| Issue number | 3 |
| Publication status | Published - Sept 2011 |
Abstract
The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(S 1) are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra (Vect(S 1) sVect(S 1))* are found.
Keywords
- Dieomorphism group of the circle, Euler equation, Integrable systems, Peakons
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Applied Mathematics
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In: Journal of Geometric Mechanics, Vol. 3, No. 3, 09.2011, p. 313-322.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Euler equations on a semi-direct product of the diffeomorphisms group by itself
AU - Escher, Joachim
AU - Ivanov, Rossen
AU - Kolev, Boris
PY - 2011/9
Y1 - 2011/9
N2 - The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(S 1) are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra (Vect(S 1) sVect(S 1))* are found.
AB - The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(S 1) are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra (Vect(S 1) sVect(S 1))* are found.
KW - Dieomorphism group of the circle
KW - Euler equation
KW - Integrable systems
KW - Peakons
UR - http://www.scopus.com/inward/record.url?scp=84866426517&partnerID=8YFLogxK
U2 - 10.3934/jgm.2011.3.313
DO - 10.3934/jgm.2011.3.313
M3 - Article
AN - SCOPUS:84866426517
VL - 3
SP - 313
EP - 322
JO - Journal of Geometric Mechanics
JF - Journal of Geometric Mechanics
SN - 1941-4889
IS - 3
ER -