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Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Author

Listed:
  • Mrutyunjaya Sahoo

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India)

  • Snehashish Chakraverty

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India)

Abstract

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots.

Suggested Citation

  • Mrutyunjaya Sahoo & Snehashish Chakraverty, 2022. "Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2900-:d:886904
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    References listed on IDEAS

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    1. Mansfield, Elizabeth L. & Clarkson, Peter A., 1997. "Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 39-55.
    2. Wazwaz, Abdul-Majid, 2008. "A study on linear and nonlinear Schrodinger equations by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1136-1142.
    3. Kangle Wang, 2022. "Fractal Solitary Wave Solutions For Fractal Nonlinear Dispersive Boussinesq-Like Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-8, June.
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