SOME COMMENTS ON THE BI(TRI)-HAMILTONIAN STRUCTURE OF GENERALIZED AKNS AND DNLS HIERARCHIES

We give the correct prescriptions for the terms involving partial deri vative(x)(-1)delta(x-y), in the Hamiltonian structures of the AKNS and DNLS systems, necessary for the Jacobi identities to hold. We establi sh that the sl(2) and sl(3) AKNS systems are tri-Hamiltonians and cons truct two compatible Hamiltonian structures for the sl(n) AKNS system. We give a method for the derivation of the recursion operator for the sl(n+1) DNLS system, and apply it explicitly to the sl(2) case, showi ng that such a system is tri-Hamiltonian. (C) 1998 Elsevier Science B. V.