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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