KdV limit for the Vlasov–Poisson–Landau system

Abstract

We are concerned with the fluid limit to KdV equations for the one-dimensional Vlasov–Poisson–Landau system that describes the dynamics of ions in plasma with the electron density determined by the self-consistent electric potential through the so-called Boltzmann relation. Formally, it is well known that as the Knudsen number $\epsilon \to 0$ the Vlasov–Poisson–Landau system in the compressible scaling converges to the Euler–Poisson equations which further under the Gardner–Morikawa transformation