  We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic
nonlinear medium including both the time relaxation of the induced nonlinearity
and the nonlocal coupling. The initial ten-dimensional FWM system can be
rewritten as a three-variable intrinsic system (namely the intensity pattern,
the amplitude of the nonlinearity and the total net gain) which is very close
to the pumped Maxwell-Bloch system. In the case of a purely nonlocal response
the initial system reduces to a real damped sine-Gordon (SG) equation. We
obtain a new solution of this equation in the form of a sech function with a
time-dependent coefficient. By applying the reductive perturbation method to
this damped SG equation, we obtain exactly the cubic complex Ginzburg Landau
equation (CGL3), but with a time dependence in the loss/gain coefficient. The
CGL3 describes the properties of the spatially localized interference pattern
formed by the FWM.
