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This article is cited in 9 scientific papers (total in 9 papers)
Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type
O. I. Mokhov Landau Institute for Theoretical Physics, Centre for Non-linear Studies
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.
Keywords:
compatible Hamiltonian operators - systems of hydrodynamic type - Lie derivative, integrable hierarchies, local Poisson brackets of hydrodynamic type, flat pencils of metrics.
Citation:
O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type”, TMF, 133:2 (2002), 279–288; Theoret. and Math. Phys., 133:2 (2002), 1557–1564
Linking options:
https://www.mathnet.ru/eng/tmf397https://doi.org/10.4213/tmf397 https://www.mathnet.ru/eng/tmf/v133/i2/p279
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