This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.

本文重点对 (3+1) 维势 Yu-Toda-Sasa-Fukuyama (YTSF) 方程的分形修正进行数值研究。提出了一种基于二尺度分形复变变换和变分原理的变分方法来求解该分形方程。通过分形复变变换，分形势-YTSF方程可转化为原势-YTSF方程。利用He提出的变分原理给出了一些分形孤子型解和分形周期波解，这些都是现有文献中没有涉及到的。Manafian 等人对原始势-YTSF 方程的变分公式和波解的一些评论。[东亚应用杂志。数学。 10 (3) (2020) 549–565] 也给出了。给出了具有不同分形维数和振幅的分形波解的数值结果来显示传播行为。