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 Zap. Nauchn. Sem. LOMI, 1988, Volume 169, Pages 44–50 (Mi znsl5595)

Integrable equations connected with the Poisson algebra

M. I. Golenishcheva-Kutuzova, A. G. Reiman

Abstract: The general $r$-matrix construction of integrable Hamiltonian systems is applied to Poisson algebras which are function algebras on symplectic manifolds with commutator given by the Poisson bracket. Two types of integrable systems are described: Hamiltonian systems on the group of symplectic diffeomorphisms whose Hamiltonians are sums of a left-invariant kinetic energy and a potential, and systems of two first order equations for two functions of one variable.

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Bibliographic databases:
UDC: 519.4

Citation: M. I. Golenishcheva-Kutuzova, A. G. Reiman, “Integrable equations connected with the Poisson algebra”, Questions of quantum field theory and statistical physics. Part 8, Zap. Nauchn. Sem. LOMI, 169, "Nauka", Leningrad. Otdel., Leningrad, 1988, 44–50

Citation in format AMSBIB
\Bibitem{GolRei88} \by M.~I.~Golenishcheva-Kutuzova, A.~G.~Reiman \paper Integrable equations connected with the Poisson algebra \inbook Questions of quantum field theory and statistical physics. Part~8 \serial Zap. Nauchn. Sem. LOMI \yr 1988 \vol 169 \pages 44--50 \publ "Nauka", Leningrad. Otdel. \publaddr Leningrad \mathnet{http://mi.mathnet.ru/znsl5595} \zmath{https://zbmath.org/?q=an:0674.58022} 

• http://mi.mathnet.ru/eng/znsl5595
• http://mi.mathnet.ru/eng/znsl/v169/p44

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This publication is cited in the following articles:
1. Theoret. and Math. Phys., 92:3 (1992), 1024–1031
2. M. A. Olshanetsky, “The large $N$ limits of integrable models”, Mosc. Math. J., 3:4 (2003), 1307–1331