高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法，基于常系数高阶色散的Ginzburg-Landau方程，通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解，给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明，在增益光纤的二阶正常色散区域，同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾；振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散

High order dispersion effect of Ginzburg-Landau equation and its self-similar analytical solutions

Using the methods based on the technique of self-similar analyzing, we find the parabolic asymptotic self-similar analytical solutions with third-order dispersion effect of constant coefficient Ginzburg-Landau equation which considers both the influence of high order dispersion and gain dispersion on the evolution of self-similar pulse. The self-similar amplitude function, phase function, strict linear chirp function and effective temporal pulse width are given in the paper. The results show that self-similar pulses still have linear chirp and remarkable third-order dispersion effect. And these theoretical results are consistent with numerical simulations.