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Zbl 0698.70013
Tu, Guizhang; Meng, Dazhi
The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. II. (English)
[J] Acta Math. Appl. Sin., Engl. Ser. 5, No.1, 89-96 (1989). ISSN 0168-9673; ISSN 1618-3932/e

Summary: [For part I see the first author, J. Math. Phys. 30, No.2, 330-338 (1989; Zbl 0678.70015).] \par 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 2000:: *70H05 Hamilton's equations
35Q99 PDE of mathematical physics and other areas
37J99 Finite-dimensional Hamiltonian etc. systems
37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.

Keywords: isospectral problem

Citations: Zbl 0678.70015

Cited in: Zbl 1014.37043 Zbl 0909.70020

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