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This article is cited in 5 scientific papers (total in 5 papers)
Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
Artur Sergyeyev Mathematical Institute, Silesian University in Opava, Na Rybnícku 1, 746 01 Opava, Czech Republic
Abstract:
We 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.
Keywords:
weakly nonlocal Hamiltonian structure; symplectic structure; Lie derivative.
Received: December 15, 2006; in final form April 23, 2007; Published online April 26, 2007
Citation:
Artur Sergyeyev, “Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility”, SIGMA, 3 (2007), 062, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma188 https://www.mathnet.ru/eng/sigma/v3/p62
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Abstract page: | 187 | Full-text PDF : | 31 | References: | 24 |
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