Abstract The propagation dynamics of solitons in Erbium-Doped Fiber Amplifiers (EDFAs) is significantly influenced by pump power, particularly within the unsaturated signal regime. Establishing this relationship is critical for the design of ultrafast signal processing systems and mode-locked fiber lasers . This study analytically and numerically investigates the formation and stability of solitary wave solutions in an EDFA governed by the modified Nonlinear Schrödinger Equation (NLSE). We first derive an expression for the pump-dependent gain coefficient, g p , from the fundamental rate equations of a three-level erbium model. Using the Bogning-Djeumen-Tchacho-Kofane (BDKm) method, we identify two distinct solution classes that exist in opposing physical regimes. First, we demonstrate that bright solitons (sech-profile) are supported in a regime of effective saturable absorption and anomalous dispersion. Numerical propagation via the Split-Step Fourier Method (SSFM) reveals that these pulses act as robust attractors but undergo adiabatic reshaping and monotonic energy decay due to the net-loss environment, with lower pump powers favoring longer propagation distances. Second, we investigate dark solitons (tanh-profile) in the normal dispersion regime under high-gain conditions. While Linear Stability Analysis (LSA) proves that the continuous-wave background is linearly stable, numerical simulations reveal the generation of persistent background oscillations. We quantitatively identify these fluctuations not as modulational instability but as perturbative radiative emission driven by the parametric mismatch between the analytical ansatz and the high-gain fiber environment. This research delineates the specific pump power boundaries and physical mechanisms required to manage optical pulse integrity in active fiber systems.
Ndichia et al. (2026) studied this question.