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The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term

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  • Zehra Pınar
  • Turgut Öziş

Abstract

It is well known that different types of exact solutions of an auxiliary equation produce new types of exact travelling wave solutions to nonlinear equations. In this paper, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term are presented to obtain novel exact solutions of the Kawahara equation. By the aid of the solutions of the original auxiliary equation, some other physically important nonlinear equations can be solved to construct novel exact solutions.

Suggested Citation

  • Zehra Pınar & Turgut Öziş, 2013. "The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, March.
    • Handle: RePEc:hin:jjmath:106349
    DOI: 10.1155/2013/106349
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    References listed on IDEAS

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    1. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    2. Zhang, Huiqun, 2009. "New exact travelling wave solutions of nonlinear evolution equation using a sub-equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 873-881.
    3. Yomba, Emmanuel, 2006. "The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer–Kaup–Kupershmidt equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 187-196.
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    Cited by:

    1. Zara, Aiman & Rehman, Shafiq Ur & Ahmad, Fayyaz & Kouser, Salima & Pervaiz, Anjum, 2022. "Numerical approximation of modified Kawahara equation using Kernel smoothing method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 169-184.
    2. El-Tantawy, S.A. & Salas, Alvaro H. & Alharthi, M.R., 2021. "Novel analytical cnoidal and solitary wave solutions of the Extended Kawahara equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Ahmad, Fayyaz & Ur Rehman, Shafiq & Zara, Aiman, 2023. "A new approach for the numerical approximation of modified Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 189-206.

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