  We investigate the nonlinear interaction between two laser beams in a plasma
in the weakly nonlinear and relativistic regime. The evolution of the laser
beams is governed by two nonlinear Schroedinger equations that are coupled with
the slow plasma density response. We study the growth rates of the Raman
forward and backward scattering instabilities as well of the Brillouin and
self-focusing/modulational instabilities. The nonlinear evolution of the
instabilities is investigated by means of direct simulations of the
time-dependent system of nonlinear equations.
