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INTEGRABLE COUPLING SYSTEMS OF HAMILTONIAN LATTICE EQUATIONS BY SEMI-DIRECT SUMS OF LIE ALGEBRAS

LI-LI ZHU

College of Information Science and Technology, Taishan College, Taian 271021, China

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JUN DU

School of Communication, Shandong Normal University, Jinan 250014, China

College of Information Science and Engineering, Shandong University, Jinan 250100, China

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XIAO-YAN MA

College of Information and Engineering, Taishan Medical University, Taian 271016, China

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, and

SHENG-JU SANG

College of Information Science and Technology, Taishan College, Taian 271021, China

School of Power Engineering, East China University of Science and Technology, Shanghai 200237, China

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https://doi.org/10.1142/S0217984910022755Cited by:0 (Source: Crossref)

Abstract

By considering a discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations are derived. The relation to the Toda type lattice is achieved by variable transformation. With the help of Tu scheme, the Hamiltonian structure of the resulting lattice hierarchy is constructed. The Liouville integrability is then demonstrated. Semi-direct sum of Lie algebras is proposed to construct discrete integrable couplings. As applications, two kinds of discrete integrable couplings of the resulting system are worked out.

Keywords:

PACS: 02.90.+p, 02.30.Ik

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