https://doi.org/10.1140/epjp/i2019-12811-y
Regular Article
A construction of new traveling wave solutions for the 2D Ginzburg-Landau equation
1
Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail, Saudi Arabia
2
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
3
Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt
* e-mail: mahmoud.abdelrahman@mans.edu.eg
Received:
28
March
2019
Accepted:
5
June
2019
Published online:
5
September
2019
In this work, three mathematical methods, namely, the Riccati-Bernoulli sub-ODE method, the 
-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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019
