On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

Yu-Feng Zhang, Honwah Tam

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)
18 Downloads (Pure)


In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple.

Original languageEnglish
Pages (from-to)335-340
Number of pages6
JournalCommunications in Theoretical Physics
Issue number3
Publication statusPublished - 1 Mar 2016

Scopus Subject Areas

  • Physics and Astronomy (miscellaneous)

User-Defined Keywords

  • discrte integrable system
  • integrable coupling
  • Lie algebra


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