Fiber lasers are a paradigm of dissipative systems, which distinguish themselves from a Hamilton system where energy is conservative. Consequently, pulses generated in a fiber laser are always accompanied by the continuous wave (CW). Under certain hypothesis, pulses generated in a fiber laser can be considered as a soliton, a product of a Hamilton system. Therefore, all the descriptions of solitons of a fiber laser are approximate. Coexistence of solitons and the CW from a fiber laser prevents unveiling of real nonlinear dynamics in fiber lasers, such as soliton interactions. Pulse behavior in a fiber laser can be represented by the state of single pulse, the state of period doubling of single pulse, the states of two pulses either tightly bound or loosely distributed, the states of three pulses, and various combinations of the above-mentioned states. Recently, soliton distillation was proposed and numerically demonstrated based on the nonlinear Fourier transform (NFT) [J. Lightwave Technol.39, 2542 (2021)JLTEDG0733-872410.1109/JLT.2021.3051036]. Solitons can be separated from the coherent CW background. Therefore, it is feasible to isolate solitons from CW background in a fiber laser. Here, we applied the NFT to various pulses generated in a fiber laser, including single pulse, single pulse in period doubling, different double pulses, and multiple pulses. Furthermore, with the approach of soliton distillation, the corresponding pure solitons of those pulses are reconstructed. Simulation results suggest that the NFT can be used to identify soliton dynamics excluding CW influence in a fiber laser, which paves a new way for uncovering real soliton interaction in nonlinear systems.