FUNCTIONAL REPRESENTATION OF THE ABLOWITZ-LADIK HIERARCHY

The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of t he inverse-scattering approach. After establishing the structure of so lutions of the auxiliary linear problems, the ALH, which has been orig inally introduced as an infinite system of differential-difference equ ations, is presented as a finite system of difference-functional equat ions. The representation obtained, when rewritten in terms of Hirota's bilinear formalism, is used to demonstrate relations between the ALH and some other integrable systems, the Kadomtsev-Petviashvilli hierarc hy in particular.