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Dynamical systems. IV: Integrable systems. (Russian) Zbl 0591.58013
Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 4, 179-248 (1985).
This is the first part of a survey on integrable dynamical systems. In the first chapter the authors deal with Hamiltonian systems and classical methods to integrate them. The second chapter deals with modern ideas for integrating evolution systems (for example Korteweg-de Vries equation), in particular methods from algebraic geometry are considered. An English translation of the article is announced to appear in 1987 (Encyclopedia of Mathematical Sciences, Springer Verlag).
Reviewer: N.Jacob

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
35Q99 Partial differential equations of mathematical physics and other areas of application
14H99 Curves in algebraic geometry
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.)
58J90 Applications of PDEs on manifolds