Hydrodynamic chains and a classification of their Poisson brackets

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.

References in corpus (6)

• On integrability of (2+1)-dimensional quasilinear systems
• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
• Classical R-matrix theory of dispersionless systems: II. (2+1)-dimension theory
• Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
• Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets

Cited by in corpus (1)

• Differential Geometry of Hydrodynamic Vlasov Equations