Dubrovin, B. A.; Novikov, S. P. 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 Cited in 8 ReviewsCited in 110 Documents MSC: 35G20 Nonlinear higher-order PDEs 76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena Keywords:Poisson brackets; Hamiltonians; hydrodynamic type; Bogolyubov-Whitman averaging method PDFBibTeX XMLCite \textit{B. A. Dubrovin} and \textit{S. P. Novikov}, Sov. Math., Dokl. 27, 665--669 (1983; Zbl 0553.35011); translation from Dokl. Akad. Nauk SSSR 270, 781--785 (1983)