Hamiltonian structure of isospectral deformation equation and semi-classical approximation to factorizedS-matrices

We consider semi-classical approximation to factorizedS-matrices. We show that this new class of matrices, calleds-matrices, defines Hamiltonian structures for isospectral deformation equations. Concrete examples of factorizeds-matrices are constructed and they are used to define Hamiltonian structure for general two-dimensional isospectral deformation systems.