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Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

Artur Sergyeyev
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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.

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Artur Sergyeyev. 2007-04-26. Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility. https://doi.org/10.3842/sigma.2007.062

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