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Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the -Expansion Method

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  • Sekson Sirisubtawee
  • Sanoe Koonprasert

Abstract

We apply the -expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

Suggested Citation

  • Sekson Sirisubtawee & Sanoe Koonprasert, 2018. "Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the -Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-15, June.
    • Handle: RePEc:hin:jnlamp:7628651
    DOI: 10.1155/2018/7628651
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    Cited by:

    1. Akram, Ghazala & Sadaf, Maasoomah & Zainab, Iqra, 2022. "Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Zainab, Iqra & Akram, Ghazala, 2023. "Effect of β-derivative on time fractional Jaulent–Miodek system under modified auxiliary equation method and exp(−g(Ω))-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Seadawy, Aly R. & Bilal, M. & Younis, M. & Rizvi, S.T.R. & Althobaiti, Saad & Makhlouf, M.M., 2021. "Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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