Thermal Science 2024 Volume 28, Issue 3 Part A, Pages: 1967-1974
https://doi.org/10.2298/TSCI2403967S
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Fractal solitary waves of the (3+1)-dimensional fractal modified KdV-Zakharov-Kuznetsov
Sun Jianshe (Institute of Mathematics and Cross Science, Jiaozuo Teacher's College, Jiaozuo, China + School of Mathematics, Jiaozuo Teacher's College, Jiaozuo, China + School of Mathematics, China University of Mining and Technology, Xuzhou, China), sunjianshe@126.com; sunjianshe@jzsz.edu.cn
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
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