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We investigate theoretically and numerically the evolutions of optical pulses in the time domain due to modulation instability (MI), where CW pump accompanied with a probe is used as the input of nonlinear fiber. As the fiber length increases, we show that it exhibits beat frequency between the pump and the probe first when the probe lies outside the MI resonance region, and then gradually transforms into a pulse train resulting from spontaneous MI rather than induced MI. However, the regular pulse train is easier to generate in the whole fiber if the probe exists in MI resonance region, and the period of the pulse train is inversely proportional to the frequency spacing between the pump and the probe. It is emphasized that the pulse period can be adjusted only when the probe is in MI resonance region. The numerical simulations are in agreement with the theoretical results. The obtained results are guidable for generating and manipulating the optical pulse train in the fiber. [ABSTRACT FROM AUTHOR]