“…Equation (2) describes the evolution of the pump power P p with the fiber length, where is the overlap factor, σ a and σ e represent the absorption and emission cross-sections, respectively, N 0 is the dopant concentration, N 2 denotes the number of excited Yb ions, which is governed by Equation (3), τ is the lifespan of the excited state population, is the reduced Planck constant, and A is the doped cross-section area. The active gain is given by Equation ( 4), which acts as a bridge between the rate equations and the GNLSE [35,36] . The SEN is approximated by a Gaussian random process with zero mean value, which satisfies [35]…”