Summary: The Karpman equation describing the interaction of a longitudinal electric field with the ion-acoustic wave in a two-component plasma, shown to be integrable by Kaup, is solved exactly both on the full-line and on the semi-line for a given (arbitrary) incident electric field in \(x=-\infty\) or \(x=0\). In particular, the method provides the explicit output values of the electric field for a plasma which is initially neutral. In the full-line case it is proved that the input electrostatic field does not generate solitons, while it does so when the problem is on the semi-line.