Abstract
In this work, three mathematical methods, namely, the Riccati-Bernoulli sub-ODE method, the $ \exp(-\varphi(\xi))$-expansion method and the sine-cosine approach, are applied for constructing many new exact solutions for the 2D Ginzburg-Landau equation. This equation is a prevalent model for the evolution of slowly varying wave packets in nonlinear dissipative media. The three proposed methods are efficient and powerful in solving a wide class of nonlinear evolution equations. In the end, three-dimensional graphs of some solutions have been plotted. Finally, we compare our results with other results in order to show that the proposed methods are robust and adequate.
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