Abstract
In this paper, we apply an analytical algorithm, namely the modified auxiliary equation method, to investigate the complex wave structures for abundant solutions related to the complex Ginzburg–Landau model. That is for studying more physical properties of this model. This model describes the wave profile showing in different physical systems. Many various formulas of solutions are obtained such as complex solitary, soliton, and exponential wave solutions. Some of the solutions are discussed by sketching them in three and two dimensional to show the dynamic of these waves. All obtained solutions are verified of its validity by using Maple software program.
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