Analytical solutions of real and imaginary parts of unstable perturbations propagating in optical fibers

Analytical solutions representing the real and imaginary parts of a perturbation field traveling in optical fibers have been derived for the linearized version of the nolinear Ｓhr-dinger equation. These generalized expressions show that the initial variations of the real and imaginary parts of the perturbation are very sensitive to the input conditions.The analytical results show that when z →∞,the gain coefficient of the perturbation approximates to g ,at the initial period the wave number k varies as-z changes, only when-z is sufficient long does the -k approximate to a constant.