2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56740This paper studies a certain completely integrable discretization of the KP hierarchy. This was constructed by Gieseker in \cite{Gie1}, from certain algebro-geometric data. This paper has the dual aim of showing that this construction is generically invertible, and obtaining explicit expressions for the flow equations. A subsequent article will discuss the Hamiltonian structure of this system.23 pages. Available also at http://www.math.metu.edu.tr/~akisiselMathematical PhysicsAlgebraic Geometrytext