Dispersive Limit of the Euler-Poisson System in Higher Dimensions

Details Dispersive Limit of the Euler-Poisson System in Higher Dimensions Dispersive Limit of the Euler-Poisson System in Higher Dimensions

2012-04-24

arxiv.org/abs/1204.5435v1

Physics

Mathematical Physics

Scientific paper

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.

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