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Exact solitary solutions for variants of the KdV equations with fractional time derivatives

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  • Odibat, Zaid M.

Abstract

In this paper, the homotopy perturbation method is implemented to construct solitary solutions for variants of the KdV equations with fractional time derivatives. In this scheme, the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Two models are investigated and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions for nonlinear problems with fractional time derivatives.

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  • Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1264-1270
    DOI: 10.1016/j.chaos.2007.08.080
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    References listed on IDEAS

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    7. 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.
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    Cited by:

    1. Gupta, A.K. & Ray, S. Saha, 2018. "On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 376-380.

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