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Traveling Wave Solutions of the Nonlinear (3 + 1)‐Dimensional Kadomtsev‐Petviashvili Equation Using the Two Variables (G′/G, 1/G)‐Expansion Method

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  • E. M. E. Zayed
  • S. A. Hoda Ibrahim
  • M. A. M. Abdelaziz

Abstract

The two variables (G′/G, 1/G)‐expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation. This method can be considered as an extension of the basic (G′/G)‐expansion method obtained recently by Wang et al. When the parameters are replaced by special values, the well‐known solitary wave solutions and the trigonometric periodic solutions of this equation were rediscovered from the traveling waves.

Suggested Citation

  • E. M. E. Zayed & S. A. Hoda Ibrahim & M. A. M. Abdelaziz, 2012. "Traveling Wave Solutions of the Nonlinear (3 + 1)‐Dimensional Kadomtsev‐Petviashvili Equation Using the Two Variables (G′/G, 1/G)‐Expansion Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:560531
    DOI: 10.1155/2012/560531
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    References listed on IDEAS

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    1. Chen, Yong & Wang, Qi, 2005. "Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1+1)-dimensional dispersive long wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 745-757.
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