r-Matrix Structure for a Restricted Flow with Bargmann Constraint

This paper deals with the integrability of a finite-dimensional IIamiltonian system linked with the gen-eralized coupled KdV hierarchy.For this purpose the associated Lax representation is presented after an elementarycalculation. It is shown that the Lax representation enjoys a synamical r-matix formula instead of a classical one in thePoisson bracket on R;.Consequently the resulting system is proved to be completely integrable in view of r-matrixstructire.