From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov

Abstract

We introduce a long wave scaling for the Vlasov-Poisson equation and derive, in the cold ions limit, 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.

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• Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations
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• Initial-Boundary Value Problems on a Half-Strip for the Generalized Kawahara-Zakharov-Kuznetsov Equation