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On the Liouville Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov-Whitham averaging theory. (English. Russian original) Zbl 0582.58012

Russ. Math. Surv. 39, No. 6, 227-228 (1984); translation from Usp. Mat. Nauk 39, No. 6(240), 209-210 (1984).
The author considers one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov-Whitham averaging theory. He solves the problem of the classification of Liouville coordinate systems arising in averaging by the Bogolyubov-Whitham method [see B. A. Dulvovin and S. P. Novikov, Dokl. Akad. Nauk SSSR 270, 781-785 (1983; Zbl 0553.35011)], and their relation with diagonalizability (i.e. integrability) of the resulting system.
Reviewer: N.Jacob

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37N99 Applications of dynamical systems

Citations:

Zbl 0553.35011
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