In this paper, we discuss the pulse dynamics of rational fraction based on the Peregrine rogue wave solution of nonlinear Schrödinger equation. Based on its properties and using the spectral filtering, the amplification of optical pulse train is proposed. The results show that the combination of a continuous-wave pump and a spectral filter positioned in fiber can act as an amplifier. And the idea is applied to the long-haul transmission of optical pulse train and four amplification periods are demonstrated. Particularly, the amplification of limited number of pulses can be realized by rectangular pulse truncation and the number of pulses can be adjusted by changing the parameters. The periodically modulated plane wave that can be controlled experimentally is taken as an input which can produce the maximumly amplified zero background pulse train and the location of maximumly amplified pulse train relates to the modulation intensity. The location of the maximumly amplified zero background pulse train changes with the modulation intensity. The results show that for two input signals with different frequencies, they can realize the amplification with the above method. By changing the modulation intensity the simultaneous amplification for two signals with different frequencies can be realized.