Coupling commutator pairs and integrable systems

Yufeng Zhang*, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1109-1120
Number of pages12
JournalChaos, Solitons and Fractals
Issue number3
Publication statusPublished - 15 Feb 2009

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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