Integrable symplectic maps associated with the ZS-AKNS spectral problem

The Darboux transformations (DTs) associated with the well-known ZS-AKNS spectral problem are regarded as discrete spectral problems. Two kinds of integrable symplectic maps are derived from them through nonlinearization procedures. As an application, they are used to calculate the finite genus solutions of some new integrable lattice models constructed from these DTs.