On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

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 A_1are defined so that the well-known Toda hierarchy and a novel discrete integrable sy...

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Bibliographic Details
Published in:Communications in theoretical physics 2016-03, Vol.65 (3), p.335-340, Article 335
Main Author: 张玉峰 Honwah Tam
Format: Article
Language:English
Subjects:
Commutators
Couplings
Hierarchies
Lie groups
Maple
Mathematical analysis
Mathematical models
Spectra
代数和
代数方程
可积系统
循环代数
扩展可积模型
换向器
离散
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Summary: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 A_1are 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 A_1,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.
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/65/3/335