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

Joachim Escher; Rossen Ivanov; Boris Kolev

doi:10.3934/jgm.2011.3.313

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

Joachim Escher, Rossen Ivanov, Boris Kolev

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	313-322
Number of pages	10
Journal	Journal of Geometric Mechanics
Volume	3
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2011.3.313 https://doi.org/10.21427/e77w-0z73
Publication status	Published - Sep 2011

Keywords

Dieomorphism group of the circle
Euler equation
Integrable systems
Peakons

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10.3934/jgm.2011.3.313
10.21427/e77w-0z73Licence: CC BY-NC-SA

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

Abstract

Keywords

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