From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov (Q387645)
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scientific article; zbMATH DE number 6242129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov |
scientific article; zbMATH DE number 6242129 |
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From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov (English)
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23 December 2013
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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.
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Vlasov-Poisson equation
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KdV equation
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Zakharov-Kuznetsov equation
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relative entropy method
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