Pulse amplification in erbium-doped fiber amplifiers is studied by considering a general model that includes both gain saturation and gain dispersion. The effects of gain dispersion are studied numerically for the case in which a fundamental soliton is launched at the amplifier input. The results show that fiber amplifiers may be useful for simultaneous amplification and compression of weak optical pulses. Under high-gain conditions the input pulse is found to split into a train of amplified subpulses whose width and repetition rate are governed by the gain bandwidth. The numerical results are in qualitative agreement with recent experiments. >