The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg–Landau equation.

中文翻译：

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复Ginzburg-Landau方程的孤子和Jacobi椭圆函数解

首先考虑了复杂的Ginzburg-Landau（CGL）方程，该方程描述了存在失谐因子时的孤子传播。然后使用改进的Jacobi椭圆展开方法系统地获得其孤子以及Jacobi椭圆函数解。在特殊情况下，当椭圆率模量趋近于1时，可以检索CGL方程的多个暗和亮孤子解。当前工作中提出的结果可以帮助完成先前对复杂的Ginzburg-Landau方程的研究。