The buildup dynamics of conventional solitons with net anomalous dispersion and dissipative solitons with normal dispersion were studied using dispersive Fourier transform technique. In order to explore how these pulses evolve with the amplification power in the optical amplifier, experiment and simulation were carried out to investigate dynamic changes of the two kinds of solitons after amplification by amplifier. The results show that spectra of the two kinds of solitons undergo different oscillations during the establishment, the spectra of conventional solitons start from a modulated beat state with violent energy oscillation then transit to a stable state, while the spectra of dissipative solitons expand steadily from a disordered modulated state to a stable state. As the pump power of the amplifier increases, for conventional soliton, the center energy of spectrum will be transferred and the spectrum will be broadened, while the spectrum of dissipative soliton will exhibit a sharp peak at the edge with unchanged spectral width. These dynamic nonlinear phenomena in mode-locked fiber lasers and optical amplifiers have potential application value in ultrafast lasers and the corresponding amplification systems.