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Variational Approach To Fractal Solitary Waves

Author

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  • JI-HUAN HE

    (Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China†School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China‡National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou 215123, P. R. China)

  • WEI-FAN HOU

    (Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China)

  • CHUN-HUI HE

    (Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China)

  • TAREQ SAEED

    (�Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • TASAWAR HAYAT

    (�Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia¶Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan)

Abstract

The morphology of a shallow-water wave is affected by the unsmooth boundary, while its peak is rarely changed. This phenomenon cannot be explained by a differential model. This paper adopts a fractal modification of the Boussinesq equation, and its traveling solitary solution is studied through its fractal variational principle, the results reveal the basic properties of solitary waves in fractal space.

Suggested Citation

  • Ji-Huan He & Wei-Fan Hou & Chun-Hui He & Tareq Saeed & Tasawar Hayat, 2021. "Variational Approach To Fractal Solitary Waves," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-5, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21501991
    DOI: 10.1142/S0218348X21501991
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    Cited by:

    1. He, Chun-Hui & Liu, Chao, 2023. "Variational principle for singular waves," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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