Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal
classification
🧮 math-ph
math.DSmath.MP
keywords
hamiltonianidealintegrablemethodoperatorssystemswellalgebraic
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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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