The one-mode and the two-mode multiboson systems with sl(2,R) symmetry are
investigated.Hamiltonians of these systems are integrated using the theory of
orthogonal polynomials. The coherent state representation for these systems is
constructed.Comment: 23 pages, 1 figur
We consider the Banach Lie-Poisson space iR ⊕ U L 1 res and its complexification C ⊕ L 1 res , where the first one of them contains the restricted Grassmannian Gr res 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.
We apply general difference calculus in order to obtain solutions to the
functional equations of the second order. We show that factorization method can
be successfully applied to the functional case. This method is equivariant
under the change of variables. Some examples of applications are presented.Comment: 22 pages, examples and new section added, several correction
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.