  We show that the KdV and the NLS equations are tri-Hamiltonian systems. We
obtain the third Hamiltonian structure for these systems and prove Jacobi
identity through the method of prolongation. The compatibility of the
Hamiltonian structures is verified directly through prolongation as well as
through the shifting of the variables. We comment on the properties of the
recursion operator as well as the connection with the two boson hierarchy.
