TY - JOUR

T1 - On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

AU - Zhang, Yu-Feng

AU - Tam, Honwah

N1 - Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - discrte integrable system

KW - integrable coupling

KW - Lie algebra

UR - http://www.scopus.com/inward/record.url?scp=84962273825&partnerID=8YFLogxK

U2 - 10.1088/0253-6102/65/3/335

DO - 10.1088/0253-6102/65/3/335

M3 - Journal article

AN - SCOPUS:84962273825

SN - 0253-6102

VL - 65

SP - 335

EP - 340

JO - Communications in Theoretical Physics

JF - Communications in Theoretical Physics

IS - 3

ER -