Weakly nonlocal Hamiltonian structures: Lie derivative and compatibility
نویسنده
چکیده
We show that under minor technical assumptions any weakly nonlocal Hamiltonian structures compatible with a given nondegenerate weakly nonlocal symplectic operator J can be written as the Lie derivatives of J 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. MSC 2000: Primary: 37K10; Secondary: 37K05.
منابع مشابه
Compatible Dubrovin–Novikov Hamiltonian operators, Lie derivative and integrable systems of hydrodynamic type
1 (Dubrovin–Novikov Hamiltonian operator [1]) is compatible with a nondegenerate local Hamiltonian operator of hydrodynamic type K 2 if and only if the operator K 1 is locally the Lie derivative of the operator K 2 along a vector field in the corresponding domain of local coordinates. This result gives, first of all, a convenient general invariant criterion of the compatibility for the Dubrovin...
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