Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

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dc.creatorSergyeyev, Artur
dc.date2006-12-15
dc.date2007-04-26
dc.date.accessioned2026-07-07T09:34:26Z
dc.date.available2026-07-07T09:34:26Z
dc.descriptionWe show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure $J$ can be written as the Lie derivative of $J^{-1}$ along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamiltonian structure of zero or first order, including Hamiltonian operators of the Dubrovin-Novikov type.
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0612048
dc.identifierhttp://arxiv.org/abs/math-ph/0612048
dc.identifierSIGMA 3 (2007), 062, 14 pages
dc.identifierdoi:10.3842/SIGMA.2007.062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159494
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleWeakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
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