Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal

Details Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal

2010-04-22

arxiv.org/abs/1004.3955v1

Physics

Mathematical Physics

36 pages

Scientific paper

By application of the coinduction method as well as Magri method to the ideal
of real Hilbert-Schmidt operators we construct the hierarchies of integrable
Hamiltonian systems on the Banach Lie-Poisson spaces which consist of these
type of operators. We also discuss their algebraic and analytic properties as
well as solve them in dimensions N=2,3,4.

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