The Hamiltonian approach in classification and integrability of hydrodynamic chains
نویسنده
چکیده
New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered.
منابع مشابه
Algebro-geometric approach in the theory of integrable hydrodynamic type systems
The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically motivated examples are investigated.
متن کاملIntegrability of the Gibbons–Tsarev system
A new approach extracting multi-parametric hydrodynamic reductions for the integrable hydrodynamic chains is presented. The Benney hydrodynamic chain is considered.
متن کاملExplicit solutions of the WDVV equation determined by the “ flat ” hydrodynamic reductions of the Egorov hydrodynamic chains . Maxim V . Pavlov
Classification of the Egorov hydrodynamic chain and corresponding 2+1 quasilinear system is given in [33]. In this paper we present a general construction of explicit solutions for the WDVV equation associated with Hamiltonian hydrodynamic reductions of these Egorov hydrodynamic chains.
متن کاملHydrodynamic chains and a classification of their Poisson brackets
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.
متن کاملA generalized hydrodynamical Gurevich-Zybin equation of Riemann type and its Lax type integrability
This paper is devoted to the study of a hydrodynamical equation of Riemann type, generalizing the remarkable Gurevich–Zybin system. This multi-component non-homogenous hydrodynamic equation is characterized by the only characteristic flow velocity. The compatible bi-Hamiltonian structures and Lax type representations of the 3-and 4-component generalized Riemann type hydrodynamical system are an...
متن کامل