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Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)‐Expansion Method

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  • Yazhou Shi
  • Xiangpeng Li
  • Ben-gong Zhang

Abstract

We employ the (G′/G)‐expansion method to seek exact traveling wave solutions of two nonlinear wave equations—Padé‐II equation and Drinfel’d‐Sokolov‐Wilson (DSW) equation. As a result, hyperbolic function solution, trigonometric function solution, and rational solution with general parameters are obtained. The interesting thing is that the exact solitary wave solutions and new exact traveling wave solutions can be obtained when the special values of the parameters are taken. Comparing with other methods, the method used in this paper is very direct. The (G′/G)‐expansion method presents wide applicability for handling nonlinear wave equations.

Suggested Citation

  • Yazhou Shi & Xiangpeng Li & Ben-gong Zhang, 2018. "Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:8583418
    DOI: 10.1155/2018/8583418
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    References listed on IDEAS

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    1. Ben-gong Zhang, 2013. "Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yao, Yuqin, 2005. "Abundant families of new traveling wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 301-307.
    3. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    4. Wazwaz, Abdul-Majid & Helal, M.A., 2005. "Nonlinear variants of the BBM equation with compact and noncompact physical structures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 767-776.
    5. Ben-gong Zhang, 2013. "Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
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