Criteria for existence of a Hamiltonian structure

2010, Volume 15, Numbers 4-5, pp. 431-439

Author(s): Bogoyavlenskij O. I., Reynolds A. P.

The necessary and sufficient conditions are derived for the existence of a Hamiltonian structure for 3-component non-diagonalizable systems of hydrodynamic type. The conditions are formulated in terms of tensor invariants defined by the metric $h_{ij}(u)$ constructed from the Haantjes (1,2)-tensor.

Keywords: Poisson brackets, conformally flat metric, covariant derivatives, Weyl–Schouten equations, Haantjes tensor

Citation: Bogoyavlenskij O. I., Reynolds A. P., Criteria for existence of a Hamiltonian structure, Regular and Chaotic Dynamics, 2010, Volume 15, Numbers 4-5, pp. 431-439

DOI: 10.1134/S1560354710040039

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