Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian

Abstract

Using the Magri method one defines an involutive family of Hamiltonians on Banach Lie-Poisson space iR+UL_res^1 (which contains the restricted Grassmannian as a symplectic leaf) and on its complexification C+L_res^1. The hierarchy of Hamilton equations given by these Hamiltonians is investigated. The operator equations of Ricatti-type are included in this hierarchy. For a few particular cases one gives the explicit solutions.

31 pages (some minor corrections and clarifications)

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