Abstract
Following the general results on the relationships about Bäcklund transformations (BTs) and exact discretisation given in a previous work [Zullo, F., “Bäcklund transformations and Hamiltonian flows” J. Phys. A: Math. Theor. 46, 145203 (2013)10.1088/1751-8113/46/14/145203], we consider the Ablowitz-Ladik hierarchy and a corresponding family of BTs. After discussing the boundary conditions, we show how to get explicit transformations. The Hamiltonian properties of the maps and of the discrete flows are examined. The conditions on the parameters of the map giving exact discretisations are discussed. Finally, analytical and numerical examples are given.
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