The optical solitons for the complex Ginzburg–Landau model with Kerr law, quadratic–cubic law and parabolic law are obtained via the $$\hbox {exp}(-\Phi (\zeta ))$$ expansion method. Many abundant solutions such as complex dark-singular, complex periodic-singular and plane-wave solutions are derived for this model. These complex solutions are useful for understanding the physical properties for this model. Figures are presented for these solutions to show the dynamics for these waves.

中文翻译：

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用 $$\hbox {exp}(-\Phi (\zeta ))$$ 展开方法在非线性光学中具有克尔、二次-三次和抛物线非线性的复杂 Ginzburg-Landau 模型的光学孤子

通过 $$\hbox {exp}(-\Phi (\zeta ))$$ 展开方法获得了具有克尔定律、二次-三次定律和抛物线定律的复杂 Ginzburg-Landau 模型的光学孤子。该模型导出了许多丰富的解，如复暗奇异解、复周期奇异解和平面波解。这些复杂的解对于理解该模型的物理属性很有用。这些解决方案的数字显示了这些波的动态。