Abstract
In this paper, we consider the long wavelength limit for the Euler-Poisson system arising in plasma including three species. It is demonstrated that when the plasma has critical densities, the modified Korteweg-de Vries (mKdV) equation can be derived, under the classical Gardner-Morikawa transform ε1/2(x−Vt)→x,ε3/2t→t as ε→0, with the velocity V depending on the densities. We estimate the error between the mKdV equation and the Euler-Poisson system in Sobolev spaces. The mKdV dynamics can be seen at time interval of order O(ε−1).
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