Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations

Abstract : This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. We investigate the special case where one of the structures is the canonical Lie-Poisson structure and the second one is constant. These structures called affine or modified Lie-Poisson structures are involved in the integrability of certain Euler equations that arise as models of shallow water waves.
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Philosophical Transactions. Series A, Mathematical, Physical and Engineering Sciences, 2007, 365 (1858), pp. 2333-2357. 〈10.1098/rsta.2007.2012〉
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Contributeur : Boris Kolev <>
Soumis le : vendredi 29 septembre 2006 - 23:33:57
Dernière modification le : mercredi 10 octobre 2018 - 01:26:53
Document(s) archivé(s) le : lundi 5 avril 2010 - 23:57:43

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Boris Kolev. Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations. Philosophical Transactions. Series A, Mathematical, Physical and Engineering Sciences, 2007, 365 (1858), pp. 2333-2357. 〈10.1098/rsta.2007.2012〉. 〈hal-00102390〉

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