Abstract: We show that when narrowband filtering and nonlinear gain are considered, long-distance propagation of stable pulses in a fiber-optic system can be realized in the presence of self-frequency shift. We analyze the system by using the perturbative approach and obtain steady-state solutions and their existence conditions. The steady-state solutions are studied by linear stability analysis. Typical examples are given for stable pulse propagation over long distances, in fiber-based transmission lines. The results are verified by direct solution of partial differential equations numerically. Finally we show that our result is also suitable for investigation of the stable soliton in fiber lasers. A typical numerical example is given.

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