Dispersive Limit of the Euler-Poisson System in Higher Dimensions

Abstract

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 ${\mathbb{R}}^2$ and the Zakharov-Kuznetsov equation in ${\mathbb{R}}^3$ for well-prepared initial data, under different scalings. This justifies rigorously the KP-II limit and the ZKE limit of the Euler-Poisson equation.