Euler equations on a semi-direct product of the diffeomorphisms group by itself

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Escher, J.; Ivanov, R.; Kolev, B.: Euler equations on a semi-direct product of the diffeomorphisms group by itself. In: Journal of Geometric Mechanics 3 (2011), Nr. 3, S. 313-322. DOI: https://doi.org/10.3934/jgm.2011.3.313

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Sum total of downloads: 60




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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.
License of this version: CC BY-NC-SA 3.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2011
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 53 88.33%
2 image of flag of Indonesia Indonesia 4 6.67%
3 image of flag of United Kingdom United Kingdom 2 3.33%
4 image of flag of United States United States 1 1.67%

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