Quasi-parabolic pulse propagation and breakup in fiber amplifiers with third-order dispersion

We present an analytical solution for propagating pulses in normal dispersion fiber amplifiers, including the effect of third-order dispersion. The solution of the generalized nonlinear Schrödinger equation is based on asymptotic methods, first-order perturbation theory, and a renormalization procedure and leads to determination of the critical length corresponding to pulse breakup. We have also found and confirmed numerically the condition on the parameters that govern the propagation, as is necessary to ensure a highly accurate analytical description of the pulses and critical lengths in fiber amplifiers with third-order dispersion.