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A construction of new traveling wave solutions for the 2D Ginzburg-Landau equation

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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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Authors and Affiliations

  1. Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail, Saudi Arabia

    S. Z. Hassan & N. A. Alyamani

  2. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Mahmoud A. E. Abdelrahman

  3. Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt

    Mahmoud A. E. Abdelrahman

Authors
  1. S. Z. Hassan
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  2. N. A. Alyamani
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  3. Mahmoud A. E. Abdelrahman
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Correspondence to Mahmoud A. E. Abdelrahman.

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Hassan, S.Z., Alyamani, N.A. & Abdelrahman, M.A.E. A construction of new traveling wave solutions for the 2D Ginzburg-Landau equation. Eur. Phys. J. Plus 134, 425 (2019). https://doi.org/10.1140/epjp/i2019-12811-y

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