  Grey solitons, with complex envelope, are obtained as exact solutions of the
coupled system describing doped optical nonlinear fibers. The phase degree of
freedom plays a crucial role in removing the restrictive equal frequency
conditions on the tanh-sech paired pulses, identified earlier [1]. The
cross-phase modulation is found to control the speed of the grey soliton, which
has an upper bound. The coupled soliton solution obtained here was found to be
stable in a wide parameter range.
