A NEW PERSPECTIVE ON THE NONLINEAR DATE–JIMBO–KASHIWARA–MIWA EQUATION IN FRACTAL MEDIA

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), 2024, vol. 32, issue 03, 1-11

Abstract: In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered two distinct solitary wave solutions, the square form of the hyperbolic secant function and the hyperbolic secant function form. Then, soliton solutions are cultivated through FVP and the minimum steady state condition. Finally, the influences of non-smooth boundaries on solitons were tackled, and the properties of the solution were demonstrated through three-dimensional contour lines. Fractal dimension can impact waveforms, but cannot affect their vertex values. The presentation of soliton solutions (SWS) using techniques is not only laudable but also noteworthy. The technique employed can also be used to investigate solitary wave solutions of other local fractional calculus partial differential equations.

Keywords: Local Fractional Derivative; Fractal Derivatives; Fractal Variational Principle; Fractal Semi-Inverse Skill; Fractal Traveling Wave Transformation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X2450066X

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