Perturbation Theory of the Nonlinear Plasma Wave with Landau Damping

A generalized Korteweg-de Vries type equation is obtained for small but finite amplitude waves in plasma by treating the Vlasov equation perturbation theoretically. The influence of ion Landau damping on the ion sound soliton is discussed. Even if the ion acoustic wave is stable, it is shown that under a certain condition the amplitude of soliton grows in time. In the case of the unstable ion acoustic wave, the amplitude of soliton saturates at the finite value.