We have analysed the output pulse characteristics of semiconductor optical amplifier (SOA). It is shown that they can be modified due to the variation of input parameters, such as, gain, input pulsewidth, input pulse energy and effects imposed by the medium. Therefore, the influence of these parameters are analysed on the output pulse shape, spectrum, chirp and pulsewidth. We have used the nonlinear propagation equation taking into account the gain spectrum dynamics, gain saturation which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. We have used the finite-difference beam propagation method to simulate the wave evolution both in time and spectral domain in the SOA. We have also simulated the four-wave mixing characteristics between pulses for various input pulses. An accurate output pulse shape can be achieved by controlling the mentioned parameters. To the authors knowledge, pulse shaping in co-propagation regime due to medium effect and input pulse shapes in presence of all nonlinear effects relevant to picosecond regime have been studied comprehensively, for the first time in this work.