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

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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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  1. Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Daniel Han-Kwan

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  1. Daniel Han-Kwan
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Communicated by P. Constantin

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Han-Kwan, D. From Vlasov–Poisson to Korteweg–de Vries and Zakharov–Kuznetsov. Commun. Math. Phys. 324, 961–993 (2013). https://doi.org/10.1007/s00220-013-1825-8

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  • DOI: https://doi.org/10.1007/s00220-013-1825-8

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