Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)

doi:10.1088/1674-1056/24/8/080201

Abstract In this paper, we first introduce a Lie algebra of the special orthogonal group, g=so(4, C), whose elements are 4×4 trace-free, skew-symmetric complex matrices. As its application, we obtain a new soliton hierarchy which is reduced to AKNS hierarchy and present its bi-Hamiltonian structure and Liouville integrability. Furthermore, for one of the equations in the resulting hierarchy, we construct a Darboux matrix T depending on the spectral parameter λ.

Keywords: zero curvature equation recursion operator Hamiltonian structure Darboux transformation

Received: 23 December 2014
Revised: 24 March 2015
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	03.65.Aa	(Quantum systems with finite Hilbert space)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61170183 and 11271007), SDUST Research Fund, China (Grant No. 2014TDJH102), the Fund from the Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province, the Promotive Research Fund for Young and Middle-aged Scientisits of Shandong Province, China (Grant No. BS2013DX012), and the Postdoctoral Fund of China (Grant No. 2014M551934).

Corresponding Authors: Wang Xin-Zeng
E-mail: wangelxz@126.com

Cite this article:

Wang Xin-Zeng (王新赠), Dong Huan-He (董焕河) Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C) 2015 Chin. Phys. B 24 080201

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Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)

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