Abstract
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.
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