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Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation

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  • Al-Mdallal, Qasem M.
  • Syam, Muhammad I.

Abstract

In this paper, we use a modified form of the Sine–Cosine method for obtaining exact soliton solutions of the generalized fifth-order nonlinear evolution equation. Analysis for this method is presented. The present method shows that the solutions involve either sec2 or sech2 under certain conditions. General forms of those conditions are determined for the first time. Exact solutions for special cases of this problem such as the Sawada-Kotera and Lax equations are determined and found to be compared well with the previous studies.

Suggested Citation

  • Al-Mdallal, Qasem M. & Syam, Muhammad I., 2007. "Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1610-1617.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:5:p:1610-1617
    DOI: 10.1016/j.chaos.2006.03.039
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    Cited by:

    1. Ye, Caier & Zhang, Weiguo, 2011. "New explicit solutions for (2+1)-dimensional soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1063-1069.
    2. He, Dongdong & Pan, Kejia, 2015. "A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 323-336.
    3. El-Nahhas, A., 2009. "Analytic approximations for the one-loop soliton solution of the Vakhnenko equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2257-2264.

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