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The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations

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  • Yusufoğlu, E.
  • Bekir, A.

Abstract

In this paper, we establish exact solutions for nonlinear evolution equations. The tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations. Many new families of exact travelling wave solutions of the Vakhnenko and modified Benjamin–Bona–Mahony (MBBM) equations are successfully obtained. The obtained solutions include solitons, solitary and periodic solutions. These solutions may be important of significance for the explanation of some practical physical problems.

Suggested Citation

  • Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1126-1133
    DOI: 10.1016/j.chaos.2007.02.004
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    References listed on IDEAS

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    1. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    2. El-Wakil, S.A. & Abdou, M.A., 2007. "New exact travelling wave solutions using modified extended tanh-function method," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 840-852.
    3. Yusufoğlu, E. & Bekir, A. & Alp, M., 2008. "Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine–Cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1193-1197.
    4. Wazwaz, Abdul-Majid, 2006. "Two reliable methods for solving variants of the KdV equation with compact and noncompact structures," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 454-462.
    5. 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.
    6. El-Wakil, S.A. & Abdou, M.A., 2007. "Modified extended tanh-function method for solving nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1256-1264.
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    Cited by:

    1. Hussain, Akhtar & Kara, A.H. & Zaman, F.D., 2023. "An invariance analysis of the Vakhnenko–Parkes Equation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Vakhnenko, V.O. & Parkes, E.J., 2012. "The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 846-852.
    4. Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.

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