从非线性薛定谔方程出发,用变分法得出了描述锐度因子为不同自然数的超高斯脉冲在光 纤色散(二阶和高阶)和非线性(三阶和五阶)作用下传输的微分方程组,用龙格-库塔算法对微分 方程组进行数值求解。结果表明对于给定的较小的光纤色散和非线性系数,都存在特定的三阶和 五阶非线性系数使非线性有效地对高阶和二阶色散给脉冲传输造成的展宽影响加以补偿,此时 超高斯脉冲在光纤以近似保形的状态稳定传输。当色散系数与非线性系数之比太大时脉冲将被无限展宽。

Based on the modified nonlinear Schrdinger equation, the evolution equations for parameters of super-Gaussian pulse with different factor of sharpness was derived under the influence of dispersion(the second-order and high-order) and nonlinearity (the third-order and quintic) by using variational method, and the evolution equations were calculated by using Runge-Kutta algorithm. The numerical results indicate that when the coefficients of dispersion and nonlinearity are small, there always exist coefficients of the third-order and the quintic nonlinearity that can compensate the influence of broadening on super-Gaussian pulse caused by the second-order and high-order dispersion effectively, in this case, the super-Gaussian pulse can transmit conformally. When the ratio of dispersion and nonlinearity is too big, the pulse is broadened infinitely.