VARIATIONAL PRINCIPLE AND SOLITARY WAVE OF THE FRACTAL FOURTH-ORDER NONLINEAR ABLOWITZ–KAUP–NEWELL–SEGUR WATER WAVE MODEL

Jianshe Sun
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Jianshe Sun: Institute of Mathematics and Cross Science, Jiaozuo Teacher’s College, Jiaozuo 454150, P. R. China2School of Mathematics, Jiaozuo Teacher’s College, Jiaozuo 454150, P. R. China3School of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-9

Abstract: In this paper, for the first time in pass records, we create the fractal fourth-order nonlinear Ablowitz–Kaup–Newell–Segur (FFONAKNS) shoal water wave mold under an unsmooth boundary or in microgravity of space. With the aid of fractal traveling wave variation (FTWV) and fractal semi-inverse technology (FSIT), the fractal variational principle (FVP) is achieved, and then, using He–Weierstrass function, the strong minimum necessary condition is proved. Afterwards, the solitary wave solution is attained by FVP and minimum stationary conditions. Finally, the effect of a non-smooth border on solitary wave is deliberated and demeanors of solutions are displayed via 3D isohypse. The fractal dimension can impact the waveform, but not its apex value. The solitary wave solution (SWS) is given, and the exhibition of the technology used is not only creditable but also significant.

Keywords: He’s Fractal Derivatives; Fractal Semi-Inverse Method; Fractal Variational Principle; He’s Weierstrass Function; Unsmooth Boundary (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500366

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