Hydrodynamic chains and a classification of their Poisson brackets

Details Hydrodynamic chains and a classification of their Poisson brackets Hydrodynamic chains and a classification of their Poisson brackets

2006-03-24

arxiv.org/abs/nlin/0603056v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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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