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Modified extended tanh-function method for solving nonlinear partial differential equations

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  • El-Wakil, S.A.
  • Abdou, M.A.

Abstract

Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers–Fisher equation and Drinfeld–Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:5:p:1256-1264
    DOI: 10.1016/j.chaos.2005.10.072
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    Cited by:

    1. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    2. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    3. Kavitha, L. & Prabhu, A. & Gopi, D., 2009. "New exact shape changing solitary solutions of a generalized Hirota equation with nonlinear inhomogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2322-2329.
    4. Haitham Qawaqneh & Jalil Manafian & Mohammed Alharthi & Yasser Alrashedi, 2024. "Stability Analysis, Modulation Instability, and Beta-Time Fractional Exact Soliton Solutions to the Van der Waals Equation," Mathematics, MDPI, vol. 12(14), pages 1-23, July.
    5. 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.

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