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

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

2009-08-19

arxiv.org/abs/0908.2738v2

J.Funct. Anal. 258(10) 3266-3294 2010

Physics

Mathematical Physics

31 pages (some minor corrections and clarifications)

Scientific paper

10.1016/j.jfa.2010.01.019

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.

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