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Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov-Whitman averaging method. (English. Russian original) Zbl 0553.35011
Sov. Math., Dokl. 27, 665-669 (1983); translation from Dokl. Akad. Nauk SSSR 270, 781-785 (1983).
Introducing the so called ”Poisson brackets of hydrodynamic type” and ”the Hamiltonians of hydrodynamic type” the authors establish a Hamiltonian formalism of one-dimensional systems of hydrodynamic type $$u^ i_ t=v^ i_ j(u)u^ j_ x$$. A pure Hamiltonian version of the Bogolyubov-Whitman averaging method and the Hamiltonian formalism of the corresponding averaged equations is also developed.
Reviewer: T.Petrila

##### MSC:
 35G20 Nonlinear higher-order PDEs 76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena