| Abstract: |
| This talk presents the long wavelength approximation limit of the Vlasov-Poisson (VP) system in torus. We derive formally two-directional wave packets as the solutions of Korteweg-de Vries (KdV) equations from 1-D VP system, the two distinct wave packets as the solutions of Zakharov-Kuznetsov (ZK) equations from 3-D VP system with magnetic field, and the two-way waves as the solutions to the corresponding Kadomtsev-Petviashvili equations from 2-D VP system without magnetic field. A rigorous justification of this long-wave limit is established by the relative entropy method. |
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