## The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. II.(English)Zbl 0698.70013

Summary: [For part I see the first author, J. Math. Phys. 30, No.2, 330-338 (1989; Zbl 0678.70015).]
An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinear evolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new one are reductions of the above hierarchy. In each case the relevant Hamiltonian form is established by making use of the trace identity.

### MSC:

 70H05 Hamilton’s equations 35Q99 Partial differential equations of mathematical physics and other areas of application 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

### Keywords:

isospectral problem

Zbl 0678.70015
Full Text:

### References:

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