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Integrable bi-Hamiltonian hierarchies generated by compatible metrics of constant Riemannian curvature. (English. Russian original) Zbl 1042.37530

Russ. Math. Surv. 57, No. 5, 999-1001 (2002); translation from Usp. Mat. Nauk 57, No. 5, 157-158 (2002).

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
53B20 Local Riemannian geometry
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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