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

We consider the Banach Lie-Poisson space and its complexification , where the first one of them contains the restricted Grassmannian Grres as a symplectic leaf. Using the Magri method we define an involutive family of Hamiltonians on these Banach Lie-Poisson spaces. 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 we give the explicit solutions.