Abstract A current driven plasma is analyzed in the two-fluid approach. A Lagrangian treatment of the charge neutral system results in a nonlinear scalar wave equation, which exhibits two different singular wave solutions. One wave collapse is associated with a density excavation, the other with a density compression. The latter represents the scenario of wave breaking and survives under charge separation. A new soliton solution is found just above threshold of linear instability of the charge nonneutral system in case of hot electrons. It is reminiscent of an ion acoustic KdV-soliton but differs from it in several respects such as in the propagation speed, in the strength and polarity of the electrostatic potential and in the spatial width. It is a finite ion temperature effect and disappears in the cold ion limit T i → 0.