Abstract
Abstract We continue the investigation of the continuum limit properties of discrete versions of the Kadomtsev-Petviashvili (KP) equation. Using a multiple-time scale expansion, in which one of the discrete variables is replaced by an infinite number of continous variables, we can derive a hierarchy of integrable equations. In this paper hierarchies associated with the 2D-Toda equation and the KP equation are treated. The direct linearization of the hierarchy is obtained applying the expansion mentioned above to the free-wave function in the integral equation. The Hamiltonian structure of the hierarchy is established via a relation between the generator of the hierarchy and an appropriate monodromy factor of the scattering problem.
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