Korteweg-De Vries Equation for Ion Acoustic Solitons in an Inhomogeneous Plasma

The modified form of the Korteweg-de Vries (KdV) equation appropriate to weakly nonlinear ion acoustic solitons in a weakly inhomogeneous plasma is derived. This equation differs from earlier versions because of the inclusion of both ion drift and ionization, which are shown to be necessary in order that the model be capable of describing an inhomogeneous plasma in a one-dimensional geometry. The soliton properties derived from this equation are shown to be significantly affected by both ion drift and ionization.