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A HIERARCHY OF LATTICE SOLITON EQUATIONS AND ITS HIGHER-ORDER SYMMETRY CONSTRAINT

XI-XIANG XU

College of Science, Shandong University of Science and Technology, Qingdao, Shandong, 266510, China

Corresponding author.

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and

HONG-XIANG YANG

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

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https://doi.org/10.1142/S021797920703720XCited by:4 (Source: Crossref)

Abstract

Starting from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is derived through a discrete zero curvature representation. The Hamiltonian structures are established for the resulting hierarchy. Then the higher-order symmetry constraint for the resulting hierarchy is studied. It is shown that under the higher-order symmetry constraint, each lattice soliton equation in the resulting hierarchy can be factored by an integrable symplectic map and a finite-dimensional Liouville integrable Hamiltonian system.

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