TY - JOUR TI - Fractal solitary waves of the (3+1)-dimensional fractal modified KdV-Zakharov-Kuznetsov AU - Sun Jianshe JN - Thermal Science PY - 2024 VL - 28 IS - 3 SP - 1967 EP - 1974 PT - Article AB - 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.