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

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

中国物理B ›› 2015, Vol. 24 ›› Issue (8): 80201-080201.doi: 10.1088/1674-1056/24/8/080201

• GENERAL • 下一篇

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

王新赠^{a b}, 董焕河^b

a State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology (SDUST), Qingdao 266590, China;
b College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266510, China

收稿日期:2014-12-23 修回日期:2015-03-24 出版日期:2015-08-05 发布日期:2015-08-05
基金资助:
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).

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

Wang Xin-Zeng (王新赠)^{a b}, Dong Huan-He (董焕河)^b

a State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology (SDUST), Qingdao 266590, China;
b College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266510, China

Received:2014-12-23 Revised:2015-03-24 Online:2015-08-05 Published:2015-08-05
Contact: Wang Xin-Zeng E-mail:wangelxz@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: zero curvature equation, recursion operator, Hamiltonian structure, Darboux transformation

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.

Key words: zero curvature equation, recursion operator, Hamiltonian structure, Darboux transformation

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

03.65.Aa (Quantum systems with finite Hilbert space)

王新赠, 董焕河. Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)[J]. 中国物理B, 2015, 24(8): 80201-080201.

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)[J]. Chin. Phys. B, 2015, 24(8): 80201-080201.

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

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

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