  A multistream model for spinless electrons in a relativistic quantum plasma
is introduced by means of a suitable fluid-like version of the
Klein-Gordon-Maxwell system. The one and two-stream cases are treated in
detail. A new linear instability condition for two-stream quantum plasmas is
obtained, generalizing the previously known non-relativistic results. In both
the one and two-stream cases, steady-state solutions reduce the model to a set
of coupled nonlinear ordinary differential equations, which can be numerically
solved, yielding a manifold of nonlinear periodic and soliton structures. The
validity conditions for the applicability of the model are addressed.
