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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 No. 3, PAGES [1967 - 1974]

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Fractal solitary waves of the (3+1)-dimensional fractal modified KdV-Zakharov-Kuznetsov

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