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A comparative study between two different methods for solving the general Korteweg–de Vries equation (GKdV)

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  • Helal, M.A.
  • Mehanna, M.S.

Abstract

The family of the KdV equations, the most famous equations embodying both nonlinearity and dispersion, has attracted enormous attention over the years and has served as the model equation for the development of soliton theory. In this paper we present a comparative study between two different methods for solving the general KdV equation, namely the numerical Crank Nicolson method, and the semi-analytic Adomian decomposition method. The stability of the numerical Crank Nicolson scheme is discussed. A comparison between the two methods is carried out to illustrate the pertinent features of the two algorithms.

Suggested Citation

  • Helal, M.A. & Mehanna, M.S., 2007. "A comparative study between two different methods for solving the general Korteweg–de Vries equation (GKdV)," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 725-739.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:3:p:725-739
    DOI: 10.1016/j.chaos.2006.11.011
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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. Syed T. R. Rizvi & Aly R. Seadawy & Shami A. M. Alsallami, 2023. "Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    3. Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif, 2019. "An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    4. Imtiaz Ahmad & Muhammad Ahsan & Zaheer-ud Din & Ahmad Masood & Poom Kumam, 2019. "An Efficient Local Formulation for Time–Dependent PDEs," Mathematics, MDPI, vol. 7(3), pages 1-18, February.

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