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Coupling commutator pairs and integrable systems

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  • Zhang, Yufeng
  • Tam, Honwah

Abstract

According to classification of the matrix Lie algebras, a type of explicit Lie algebras are constructed which can be decomposed into a few Lie subalgebras. These subalgebras constitute several coupling commutator pairs from which some continuous multi-integrable couplings could be generated if the proper isospectral Lax pairs could be set up. Then the above Lie algebras are again decomposed into a kind of Lie algebras which are also closed under the matrix multiplication. From such the Lie algebras, some discrete multi-integrable couplings could be worked out. Finally, a few examples are given. However, the Hamiltonian structures of the (continuous and discrete) integrable couplings obtained by the above Lie algebras cannot be computed by using the trace identity or the quadratic-form identity, which is a strange and interesting problem. The phenomenon indicates that the importance of the Lie-algebra classification. The problem also needs us to try to find an efficient scheme to deal with.

Suggested Citation

  • Zhang, Yufeng & Tam, Honwah, 2009. "Coupling commutator pairs and integrable systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1109-1120.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1109-1120
    DOI: 10.1016/j.chaos.2007.04.027
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    References listed on IDEAS

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    1. Guo, Fukui & Zhang, Yufeng, 2007. "The integrable coupling of the AKNS hierarchy and its Hamiltonian structure," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1898-1902.
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    Cited by:

    1. Ma, Wen-Xiu & Meng, Jinghan & Zhang, Mengshu, 2016. "Nonlinear bi-integrable couplings with Hamiltonian structures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 166-177.

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