A generalized AKNS hierarchy and its bi-Hamiltonian structures

Tiecheng Xia, Fucai You and Dengyuan Chen

Chaos, Solitons & Fractals, 2005, vol. 23, issue 5, 1911-1919

Abstract: First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:23:y:2005:i:5:p:1911-1919

DOI: 10.1016/j.chaos.2004.07.004

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