Document Type

Journal Article

Department/Unit

Department of Computer Science

Abstract

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.

Publication Year

2016

Journal Title

Communications in Theoretical Physics

Volume number

65

Issue number

3

Publisher

IOP Publishing

First Page (page number)

335

Last Page (page number)

340

Referreed

1

DOI

10.1088/0253-6102/65/3/335

ISSN (print)

02536102

Link to Publisher’s Edition

http://dx.doi.org/10.1088/0253-6102/65/3/335

Keywords

discrte integrable system, Lie algebra, integrable coupling

Available for download on Saturday, April 01, 2017

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