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Hydrodynamic chains and a classification of their Poisson brackets

Maxim V. Pavlov
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Abstract

Necessary and sufficient conditions for an existence of the Poisson brackets significantly simplify in the Liouville coordinates. The corresponding equations can be integrated. Thus, a description of local Hamiltonian structures is a first step in a description of integrable hydrodynamic chains. The concept of $M$ Poisson bracket is introduced. Several new Poisson brackets are presented.

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Maxim V. Pavlov. 2006-03-24. Hydrodynamic chains and a classification of their Poisson brackets. https://doi.org/10.1063/1.2399086

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