Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

Artur Sergyeyev

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

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.

Détail

Keywords: weakly nonlocal Hamiltonian structure; symplectic structure; Lie derivative.

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