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A Liouville integrable Hamiltonian system associated with a generalized Kaup–Newell spectral problem

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  • Fan, Engui

Abstract

Starting from a generalized Kaup–Newell spectral problem involving an arbitrary function, we derive a hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as Kaup–Newell equation, Chen–Lee–Liu equation, Gerdjikov–Ivanov equation, Burgers equation, modified Korteweg–de Vries equation and Sharma–Tasso–Olever equation. It is also shown that the hierarchy is integrable in Liouville's sense and possesses multi-Hamiltonian structure.

Suggested Citation

  • Fan, Engui, 2001. "A Liouville integrable Hamiltonian system associated with a generalized Kaup–Newell spectral problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 105-113.
    • Handle: RePEc:eee:phsmap:v:301:y:2001:i:1:p:105-113
    DOI: 10.1016/S0378-4371(01)00360-0
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    Citations

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    Cited by:

    1. Li, Zhu & Dong, Huanhe, 2008. "A Liouville integrable system and its bi-Hamiltonian structure," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 252-261.
    2. Chao, Yue & Zhang, Yufeng, 2007. "A higher-dimensional multi-component integrable hierarchy and its integrable couplings," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1477-1484.
    3. Li, Zhu & Dong, Huanhe, 2008. "(2+1)-Dimensional Dirac hierarchy and its integrable couplings as well as multi-component integrable system," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 574-580.
    4. Yu, Fajun & Zhang, Hongqing, 2009. "Constructing the multicomponent coupling Davey–Stewardson (DS) hierarchy with pseudodifferential operator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1867-1876.
    5. Zhang, Yufeng & Guo, Xiurong, 2006. "A (2+1)-dimensional integrable hierarchy and its extending integrable model," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 555-559.
    6. Zhang, Yu-Feng & Nian, Si-Hong & Fan, En-Gui, 2007. "A solitary hierarchy of an integrable coupling and its Hamiltonian structure," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 914-918.
    7. Fan, Engui & Zhang, Yufeng, 2006. "Vector loop algebra and its applications to integrable system," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 966-971.
    8. Chao, Yue, 2007. "Using a multi-component loop algebra to obtain an integrable extension of the KN hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 940-944.
    9. Guo, Fukui & Zhang, Yufeng, 2009. "A direct method for producing Hamiltonian structure of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 436-439.

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