Propagation of solitary wave in non-uniform fiber system with high-order nonlinear effects

The ultra-short pulse propagation in a non-uniform fiber system is investigated based on the variable coefficient coupled higher-order nonlinear Schrödinger equation with the dispersion gain and nonlinear gain terms. By using the ansatz method and the split-step Fourier method, we get the exact solitary wave solution, with which the transmission process of the solitary wave is studied. Furthermore we obtain the stability of the solitary wave under finite initial perturbations. The interaction between two neighboring solitary waves is also studied.