VARIATIONAL APPROACH TO FRACTAL SOLITARY WAVES

Ji-Huan He, Wei-Fan Hou, Chun-Hui He, Tareq Saeed () and Tasawar Hayat
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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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-5

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.

Keywords: Soliton; Two-Scale Fractal Derivative; Fractal Complex Transform; Fractal Variational Theory (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501991

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