Abstract
The Lax pair of a lattice equation is given by a discrete spectral problem and the negative Kaup–Newell spectral problem. Based on the Lax nonlinearization technique, they are transformed into a symplectic map and a Hamiltonian system, which are integrable in the Liouville sense and are straightened out in the Jacobi coordinates. An algebraic–geometric solution of the lattice equation is obtained by the Riemann–Jacobi inversion. Explicit solutions of the associated lattice hierarchy are given.
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