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On the solitary wave solution of fractional Kudryashov–Sinelshchikov equation describing nonlinear wave processes in a liquid containing gas bubbles

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  • Gupta, A.K.
  • Saha Ray, S.

Abstract

In the present paper, the nonlinear time-fractional Kudryashov–Sinelshchikov equation has been solved numerically by using radial basis function (RBF) method. The RBF method is successfully implemented to the time-fractional Kudryashov–Sinelshchikov equation in order to achieve its approximate solution. As the exact solution of fractional Kudryashov–Sinelshchikov equation is not recorded earlier in literature, the analytical exact solutions have been constructed by using sech-tanh method via fractional complex transform. The numerical outcomes obtained by RBF are observed to be in good agreement with the exact solutions as well as with the acquired sech-tanh solutions.

Suggested Citation

  • Gupta, A.K. & Saha Ray, S., 2017. "On the solitary wave solution of fractional Kudryashov–Sinelshchikov equation describing nonlinear wave processes in a liquid containing gas bubbles," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 1-12.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:1-12
    DOI: 10.1016/j.amc.2016.11.003
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Shokri, Ali, 2008. "A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 700-715.
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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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