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The Lie-Poisson representation of the nonlinearized eigenvalue problem of the Kac-van Moerbeke hierarchy. (English) Zbl 0972.37050

Summary: The Kac-van Moerbeke hierarchy is studied by a 3\(\times\)3 discrete eigenvalue problem and the corresponding nonlinearized one an integrable Poisson map with a Lie-Poisson structure is also presented. Moreover, the 2\(\times\)2 nonlinearized eigenvalue problem associated with the Kac-van Moerbeke hierarchy is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.

MSC:

37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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