THE DEDUCTION OF THE LAX REPRESENTATION FOR CONSTRAINED FLOWS FROM THE ADJOINT REPRESENTATION

For x- and t(n)-finite-dimensional Hamiltonian systems obtained from the decompositions of zero-curvature equations, it is shown that their Lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems. As a consequence, the zero-curvature representation for soliton hierarchy with source is presented.