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Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system

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  • Ali, Ahmad T.
  • Khater, Mostafa M.A.
  • Attia, Raghda A.M.
  • Abdel-Aty, Abdel-Haleem
  • Lu, Dianchen

Abstract

This research paper investigates the analytical and numerical solutions of the generalized formula of Hirota-Satsuma coupled KdV system which is also known as the generalized KdV equation that is derived by R. Hirota and J. Satsuma. The modified Khater method and B-spline scheme are used to earn abundant of computational and approximate solutions on this model. This equation characterizes an interaction of two long undulations with diverse dispersion kinsmen. The comparison between our obtained computational and numerical solutions to clarify the convergence of solutions is explained and discussed. For more explanation of the model’s physical properties, some of the obtained solutions are sketched in different types, and the comparison between the computational and numerical solutions are explained by showing the values of absolute error between them. The performance of both used method is effective, powerful, and shows its ability to apply to many nonlinear evolution equations.

Suggested Citation

  • Ali, Ahmad T. & Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Lu, Dianchen, 2020. "Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304199
    DOI: 10.1016/j.chaos.2019.109473
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    References listed on IDEAS

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    1. Osman, M.S. & Wazwaz, Abdul-Majid, 2018. "An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 282-289.
    2. Saberi, Elaheh & Reza Hejazi, S., 2018. "Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota–Satsuma coupled KdV system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 296-307.
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    Cited by:

    1. Appanah Rao Appadu & Abey Sherif Kelil, 2020. "On Semi-Analytical Solutions for Linearized Dispersive KdV Equations," Mathematics, MDPI, vol. 8(10), pages 1-34, October.
    2. Khater, Mostafa M.A. & Mohamed, Mohamed S. & Attia, Raghda A.M., 2021. "On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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