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

Abstract : The geodesic equations of a class of right invariant metrics on the semi-direct product of the diffeomorphisms group of the circle by itself (acting by conjugacy) 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 are found.
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Journal of Geometric Mechanics, American Institute of Mathematical Sciences (AIMS), 2011, 3 (3), pp.313 - 322. 〈10.3934/jgm.2011.3.313〉
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Contributeur : Boris Kolev <>
Soumis le : samedi 19 novembre 2011 - 22:54:46
Dernière modification le : mercredi 10 octobre 2018 - 01:26:22

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Boris Kolev, Joachim Escher, Rossen Ivanov. Euler equations on a semi-direct product of the diffeomorphisms group by itself. Journal of Geometric Mechanics, American Institute of Mathematical Sciences (AIMS), 2011, 3 (3), pp.313 - 322. 〈10.3934/jgm.2011.3.313〉. 〈hal-00642934〉

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