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From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov. (English) Zbl 1284.35439

The author introduces a long wave scaling for the Vlasov-Poisson equation (which describes the evolution of ions in a plasma) and derive, in the cold ions limit (which means that the ions have zero kinetic temperature), the Korteweg-de Vries equation in 1D and the Zakharov-Kuznetsov equation in higher dimensions, in the presence of an external magnetic field. The proofs are based on the relative entropy method.

MSC:

35Q83 Vlasov equations
35Q53 KdV equations (Korteweg-de Vries equations)
82D10 Statistical mechanics of plasmas
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