Compatible Dubrovin–Novikov Hamiltonian Operators,Lie Derivative,and Integrable Systems of Hydrodynamic Type |
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Authors: | O. I. Mokhov |
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Affiliation: | (1) Landau Institute for Theoretical Physics, RAS, Moscow, Russia |
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Abstract: | We prove that two Dubrovin–Novikov Hamiltonian operators are compatible if and only if one of these operators is the Lie derivative of the other operator along a certain vector field. We consider the class of flat manifolds, which correspond to arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. Locally, these manifolds are defined by solutions of a system of nonlinear equations, which is integrable by the method of the inverse scattering problem. We construct the integrable hierarchies generated by arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. |
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Keywords: | compatible Hamiltonian operators systems of hydrodynamic type Lie derivative integrable hierarchies local Poisson brackets of hydrodynamic type flat pencils of metrics |
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