  The nonlinear evolution of the quantum two-stream instability in a plasma
with counter-streaming electron beams is studied. It is shown that in the
long-wave limit the nonlinear stage of the instability can be described by the
elliptic nonlinear string equation. We present two types of the nonlinear
solutions. The first one is an unstable nonlinear mode that is continuously
related with the growing linear solution and the second one is a pulsating
soliton. We show that both of these solutions blow up in a finite time.
