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Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy

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Listed:
  • Zhengduo Shan
  • Hongwei Yang
  • Baoshu Yin

Abstract

With the help of the known Lie algebra, a type of new 8‐dimensional matrix Lie algebra is constructed in the paper. By using the 8‐dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati‐Konno‐Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.

Suggested Citation

  • Zhengduo Shan & Hongwei Yang & Baoshu Yin, 2014. "Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:678725
    DOI: 10.1155/2014/678725
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    References listed on IDEAS

    as
    1. Zhang, Yufeng & Guo, Fukui, 2007. "Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 490-495.
    2. Fan, Engui & Zhang, Yufeng, 2006. "Vector loop algebra and its applications to integrable system," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 966-971.
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