1. From Vlasov–Poisson to Korteweg–de Vries and Zakharov–Kuznetsov
- Author
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Daniel Han-Kwan, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
- Subjects
Kullback–Leibler divergence ,Mathematics::Analysis of PDEs ,Complex system ,FOS: Physical sciences ,Poisson distribution ,01 natural sciences ,symbols.namesake ,Mathematics - Analysis of PDEs ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Physics::Plasma Physics ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Limit (mathematics) ,0101 mathematics ,Scaling ,Mathematical Physics ,Mathematical physics ,Vries equation ,Physics ,010102 general mathematics ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Magnetic field ,010101 applied mathematics ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symbols ,Analysis of PDEs (math.AP) - 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.
- Published
- 2013
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