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Application of a semi-direct sum of Lie algebras to the TD hierarchy

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  • You, Fucai
  • Xia, Tiecheng

Abstract

We construct a Lie algebra G by using a semi-direct sum of Lie algebra G1 with Lie algebra G2. A direct application to the TD hierarchy leads to a novel hierarchy of integrable couplings of the TD hierarchy. Furthermore, the generalized variational identity is applied to Lie algebra G to obtain quasi-Hamiltonian structures of the associated integrable couplings.

Suggested Citation

  • You, Fucai & Xia, Tiecheng, 2009. "Application of a semi-direct sum of Lie algebras to the TD hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2750-2755.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2750-2755
    DOI: 10.1016/j.chaos.2008.10.009
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    References listed on IDEAS

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    1. You, Fucai & Xia, Tiecheng, 2008. "The integrable couplings of the generalized coupled Burgers hierarchy and its Hamiltonian structures," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 953-960.
    2. Xia, Tiecheng & You, Fucai, 2006. "A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 938-948.
    3. Xia, Tiecheng & You, Fucai & Chen, Dengyuan, 2005. "A generalized AKNS hierarchy and its bi-Hamiltonian structures," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1911-1919.
    4. You, Fucai & Xia, Tiecheng, 2008. "A new loop algebra A∼5 and its applications to integrable system," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1481-1488.
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