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

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dc.creatorKolev, Boris
dc.date2006-09-30
dc.date.accessioned2026-07-07T08:26:57Z
dc.date.available2026-07-07T08:26:57Z
dc.descriptionThis 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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0610001
dc.identifierhttp://arxiv.org/abs/math-ph/0610001
dc.identifierPhilosophical Transactions. Series A, Mathematical, Physical and Engineering Sciences 365, 1858 (2007) pp. 2333-2357
dc.identifierdoi:10.1098/rsta.2007.2012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137119
dc.subjectMathematical Physics
dc.subject35Q35, 35Q53, 37K10, 37K65
dc.titleBi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations
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