Abstract
It is studied here how the Ablowitz-Ladik (AL) hierarchy and their restricted flows are related to the AKNS hierarchy and to their restricted flows in the continuous limit. It is shown that restricted flows of the AL hierarchy yield discrete maps approximating restricted flows of the AKNS hierarchy. Integrals of motion and Lax representation for restricted flows of the AL hierarchy as well as a discrete zero-curvature representation for the AL hierarchy with sources are given.
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