  In this paper, we consider the dispersive limit of the Euler-Poisson system
for ion-acoustic waves. We establish that under the Gardner-Morikawa type
transformations, the solutions of the Euler-Poisson system converge globally to
the Kadomtsev-Petviashvili II equation in $\Bbb R^2$ and the Zakharov-Kuznetsov
equation in $\Bbb R^3$ for well-prepared initial data, under different
scalings. This justifies rigorously the KP-II limit and the ZKE limit of the
Euler-Poisson equation.
