EXACT TRAVELING WAVE SOLUTION OF GENERALIZED (4+1)-DIMENSIONAL LOCAL FRACTIONAL FOKAS EQUATION

Zhuo Jiang, Zong-Guo Zhang and Xiao-Feng Han
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Zhuo Jiang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China
Zong-Guo Zhang: Division of Mathematics and Artificial Intelligence, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China
Xiao-Feng Han: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-9

Abstract: In this paper, within the scope of the local fractional derivative theory, the (4+1)-dimensional local fractional Fokas equation is researched. The study of exact solutions of high-dimensional nonlinear partial differential equations plays an important role in understanding complex physical phenomena in reality. In this paper, the exact traveling wave solution of generalized functions is analyzed defined on Cantor sets in high-dimensional integrable systems. The results of non-differentiable solutions in different cases are numerically simulated when the fractal dimension is equal to Ï = ln 2/ln 3. The results show that the exact solution of the local fractional Fokas equation represents the fractal waves on the shallow water surface. Through numerical simulation, we find that the exact solution of the local fractional Fokas equation can describe the fractal waves and waves characteristics of shallow water surface. It also shows that the study of traveling wave solutions of nonlinear local fractional equations has important significance in mathematical physics.

Keywords: (4+1)-Dimensional Local Fractional Fokas Equation; Fractal Wave; Traveling Wave Solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401151

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