Nonlinear Ion Acoustic Waves with Landau Damping

Abstract

The Korteweg-de Vries equation for the ion acoustic wave, modifield to include the effects of ion and electron linear Landau damping, is rigorously derived from the Vlasov-Poisson equations by a multi-scale asymptotic expansion method. Careful examination of the various orderings also shows that non-linear resonance effects (trapping, reflection) can be significant.