Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies

Details Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies

1997-01-20

arxiv.org/abs/solv-int/9701012v1

Phys.Lett. A237 (1998) 225-233

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, LaTex

Scientific paper

We give the correct prescriptions for the terms involving the inverse of the derivative of the delta function, in the Hamiltonian structures of the AKNS and DNLS systems, in order for the Jacobi identities to hold. We also establish that the sl(2) AKNS and DNLS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(3) AKNS system. We also give a derivation of the recursion operator for the sl(n+1) DNLS system.

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