THERMAL SCIENCE

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Jianshe Sun

FRACTAL SOLITARY WAVES OF THE (3+1)-DIMENSIONAL FRACTAL MODIFIED KDV-ZAKHAROV-KUZNETSOV

ABSTRACT
In this work, the fractal (3+1)-D modified KdV-Zakharov-Kuznetsov (MKdV-ZK) model is studied, which can represent weakly non-linear waves under the unsmooth boundary. With the help of the fractal traveling wave transformation and the semi-inverse method, a fractal variational principle is obtained, which is a strong minimum one according to the He-Weierstrass function. From the variational principle, a fractal solitary wave solution is obtained, and the influence of un-smooth boundary on solitary waves is studied and the behaviors of the solutions are presented via 3-D plots. This paper shows that the fractal dimensions can affect the wave pattern, but cannot influence its crest value.
KEYWORDS
He’s fractal derivatives, fractal variational principle, semi-inverse method, unsmooth boundary, He-Weierstrass function
PAPER SUBMITTED: 2022-11-08
PAPER REVISED: 2023-03-29
PAPER ACCEPTED: 2023-05-29
PUBLISHED ONLINE: 2024-05-18
DOI REFERENCE: https://doi.org/10.2298/TSCI2403967S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 3, PAGES [1967 - 1974]
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Fractal solitary waves of the (3+1)-dimensional fractal modified KdV-Zakharov-Kuznetsov

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence