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A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system

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  • Xia, Tiecheng
  • You, Fucai

Abstract

A subalgebra of higher-dimension loop algebra A2˜ is constructed, from which a new 3×3 isospectral problem is designed. By making use of Tu’s scheme, an integrable Hamiltonian hierarchy of equations in the sense of Liouville is obtained, which possesses tri-Hamiltonian structure. As reduction cases of the hierarchy presented in this paper, the generalized MKdV equation is engendered. By establishing binary symmetric constraints, three constrained flows of the hierarchy are presented, which are then reduced to Hamiltonian systems. Finally, an integrable coupling system is obtained by constructing a high-dimension loop algebra.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:938-948
    DOI: 10.1016/j.chaos.2005.09.016
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    Cited by:

    1. 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.
    2. Zhang, Jiao, 2009. "The integrable couplings of the Modified Jaulent–Miodek hierarchy and its Hamiltonian structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 138-144.
    3. 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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