A theory, combining the relations of pulse traveling into quantum dot (QD) semiconductor optical amplifier (SOA) with the four-wave mixing (FWM) theory in these SOAs, is developed. Carrier density pulsation (CDP), carrier heating (CH), and spectral hole burning (SHB) contributions on FWM efficiency are discussed. Effect of QD ground state and wetting layer are included. An additional parameter appears in the gain integral relation of QD SOAs. An equation formulating pulses in the QD SOAs is introduced. We have found that FWM in QD SOAs is detuning and is pulse width dependent. For short pulses, CH is dominant at high detunings (10-100 GHz) while at higher detunings (>100 GHz) the SHB is the dominant one. Undesired paunch behavior is shown in QD SOAs then, CDP must be reduced. (C) 2014 Elsevier B.V. All rights reserved.