A STUDY ON INFINITE NUMBER OF INTEGRALS O F MOTION IN CLASSICALLY INTEGRABLE SYSTEM WITH BOUNDARY (I)

By the zero curvature condition in classically integrable system, the generating functions for integrals of motion and equations for solving K+/- matrices are obtained in two-dimensional integrable systems on a finite intervel with independent boundary conditions on each end. Cla ssically integrable boundary conditions will be found by solving K+/- matrices. Zn this paper, we develop a Hamiltonian method in classicall y integrable system with independent boundary conditions on eath end. Our result can be applied to more integrable systems than those associ ated with E.K. Sklyanin's approach.