From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
  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. 
Daniel Han-Kwan (DMA)
math.AP math-ph math.MP