A theoretical model for analyzing the combined effects of amplified spontaneous emission (ASE) and intraband process on the propagation of pulses through SOA is presented. An analysis for the differential equations and the related parameters that describe the self phase modulation SPM in SOA is presented. Moreover, the effects of these variations on the pulse shape and spectrum is explained. A method for driving the coupled propagation equations of the FWM process in SOA (for the case of the pump-probe configuration) is proposed, which can be extended to find the propagation equations of any number of signals. SOA is divided theoretically into many segments in longitudinal z direction, so that the pump power change in each segment can be considered very small , this leads to solving the coupled propagation equations analytically.