We have theoretically studied pulse propagation in a normal-dispersion optical cubicon fiber amplifier (NDOCFA) with
an arbitrary longitudinal gain proflie, and have obtained an analytic solution for the nonlinear Schrödinger equation that
describles such an amplifier. The results show that the characteristics of self-similarity and linear chirp will be lost due to
third-order dispersion. However, by using a dispersion compensation technique, one can obtain efficient and high-quality
compressed pulses. The numerical simulation is consistent with the analytic results.
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