SEMI-DOMAIN SOLUTIONS TO THE FRACTAL (3+1)-DIMENSIONAL JIMBO–MIWA EQUATION

Peng Xu, Huan Huang and Hui Liu
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Peng Xu: School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, P. R. China
Huan Huang: School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, P. R. China
Hui Liu: School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-8

Abstract: In this work, the variational direct method (VDM) based on the variational theory and Ritz-like method, combined with the fractal two-scale transformation, is employed to construct the semi-domain solutions of the (3+1)-dimensional fractal Jimbo–Miwa (JM) equation, which is derived by He’s fractal derivative. The applicability and effectiveness of the acquired solutions on the Cantor sets are presented through the numerical results in the form of 3-dimensional graphs. In addition, as a comparison, the exact solutions of the classic (3+1)-dimensional JM equation for γ = 1 are also illustrated. The obtained results in this work are expected to open new perspectives for the traveling wave theory.

Keywords: Semi-Domain Solutions; Semi-Inverse Method; Variational Principle; Jimbo–Miwa Equation; Variational Direct Method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400425

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