An integrable lattice equation related to the nKN system

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.