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Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the (G′/G2)‐Expansion Method

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  • Sekson Sirisubtawee
  • Sanoe Koonprasert

Abstract

We apply the (G′/G2)‐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 (G′/G2)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:7628651
    DOI: 10.1155/2018/7628651
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    References listed on IDEAS

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    1. Agrawal, Manish & Jog, C.S., 2017. "A quadratic time finite element method for nonlinear elastodynamics within the context of hybrid finite elements," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 203-220.
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    Cited by:

    1. Samina, Samina & Wali, Samad, 2026. "Chaotic dynamics and Lyapunov analysis of the Benney–Luke equation for image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 683(C).

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