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Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation

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  • Xiao-Jun Yang
  • Jordan Hristov
  • H. M. Srivastava
  • Bashir Ahmad

Abstract

A mathematical model of fractal waves on shallow water surfaces is developed by using the concepts of local fractional calculus. The derivations of linear and nonlinear local fractional versions of the Korteweg-de Vries equation describing fractal waves on shallow water surfaces are obtained.

Suggested Citation

  • Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    • Handle: RePEc:hin:jnlaaa:278672
    DOI: 10.1155/2014/278672
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    Cited by:

    1. Heydari, M.H. & Razzaghi, M. & Avazzadeh, Z., 2021. "Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
    3. Hari M. Srivastava & Khaled Mohammed Saad & Walid M. Hamanah, 2022. "Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations," Mathematics, MDPI, vol. 10(7), pages 1-13, March.
    4. Spineanu, F. & Vlad, M., 2015. "Self-organization of the vorticity field in two-dimensional quasi-ideal fluids: The statistical and field-theoretical formulations," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 473-479.

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