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We focus on several aspects conceing the numerical simulation of a passively mode-locked Yb-doped fiber laser by a non-distributed model.The characteristics of soliton evolution in a wave-breaking-free regime are numerically investigated with the split-step Fourier method.Based on the model,a parabolic-shaped soliton with a nearlylinear chirp and bound soliton pairs are obtained by controlling the intra-cavity average dispersion of the fiber laser.A phenomenon is observed that by keeping the system parameters unchanged,linearly chirped parabolic soliton and bound soliton pairs are attainable under different initial conditions in the transient region between these two kinds of solitons.