KdV limit of the Euler-Poisson system

Consider the scaling ${\epsilon }^{1\mathrm{/}2}(x-Vt)\to x,{\epsilon }^{3\mathrm{/}2}t\to t$ in the Euler-Poisson system for ion-acoustic waves \eqref{equ1}. We establish that as $\epsilon \to 0$, the solutions to such Euler-Poisson system converge globally in time to the solutions of the Korteweg-de Vries equation.