Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

Details Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

2006-12-15

arxiv.org/abs/math-ph/0612048v2

SIGMA 3 (2007), 062, 14 pages

Physics

Mathematical Physics

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.062

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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