CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 2 APRIL 2002

New Lax Integrable Hierarchies and Liouville Integrable Bi-Hamiltonian Structures Associated with an Isospectral Problem

Zhenya Yan^*

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
(Received September 24, 2001)

A new Lax integrable hierarchy associated with a properly isospectral problem with an arbitrary function, which contains the Dirac isospectral problem, is presented in this paper. As a reduction, a representative system of the generalized nonlinear Schrödinger equations in the hierarchy is explicitly given. It is shown that the Lax integrable hierarchy possesses a bi-Hamiltonian structure by using the trace identity method. In addition, it is proved that the Lax integrable hierarchy is also Liouville integrable.

PACS. 03.40.Kf - Waves and wave propagation: general mathematical aspects.

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