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Expansion of the Lie algebra and its applications

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  • Guo, Fukui
  • Zhang, Yufeng

Abstract

We take the Lie algebra A1 as an example to illustrate a detail approach for expanding a finite dimensional Lie algebra into a higher-dimensional one. By making use of the late and its resulting loop algebra, a few linear isospectral problems with multi-component potential functions are established. It follows from them that some new integrable hierarchies of soliton equations are worked out. In addition, various Lie algebras may be constructed for which the integrable couplings of soliton equations are obtained by employing the expanding technique of the the Lie algebras.

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  • Guo, Fukui & Zhang, Yufeng, 2006. "Expansion of the Lie algebra and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1048-1055.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:1048-1055
    DOI: 10.1016/j.chaos.2005.04.073
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    Cited by:

    1. Guo, Fukui & Zhang, Yufeng, 2008. "The computational formula on the constant γ appeared in the equivalently used trace identity and quadratic-form identity," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 499-505.
    2. Dong, Huan-he & Wang, Xiang-rong, 2008. "The quadratic-form identity for constructing Hamiltonian structures of the NLS–MKdV hierarchy and multi-component Levi hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 245-251.

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