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Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations

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  • Zhou, Jiangrui
  • Zhou, Rui
  • Zhu, Shihui

Abstract

The fourth-order complete discrimination system method is employed to the seek exact solutions of the Tzitzeica–Dodd–Bullough equation as well as the double sinh-Gordon equation. We obtain a range of new solutions, including a periodic solution, a triangular function solution, rational function solutions, peakon solutions and Jacobian elliptic function solutions.

Suggested Citation

  • Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308122
    DOI: 10.1016/j.chaos.2020.110419
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Guicheng Shen & Yunchuan Sun & Yongping Xiong, 2013. "New Travelling-Wave Solutions for Dodd-Bullough Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, July.
    3. Wazwaz, Abdul-Majid, 2005. "The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 55-63.
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    Cited by:

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    2. Tang, Lu, 2022. "Bifurcation analysis and multiple solitons in birefringent fibers with coupled Schrödinger-Hirota equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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