In this paper, within the scope of the local fractional derivative theory, the (4+1)-dimensional local fractional Fokas equation is researched. The study of exact solutions of high-dimensional nonlinear partial differential equations plays an important role in understanding complex physical phenomena in reality. In this paper, the exact traveling wave solution of generalized functions is analyzed defined on Cantor sets in high-dimensional integrable systems. The results of non-differentiable solutions in different cases are numerically simulated when the fractal dimension is equal to $\rho =ln2/ln3$. The results show that the exact solution of the local fractional Fokas equation represents the fractal waves on the shallow water surface. Through numerical simulation, we find that the exact solution of the local fractional Fokas equation can describe the fractal waves and waves characteristics of shallow water surface. It also shows that the study of traveling wave solutions of nonlinear local fractional equations has important significance in mathematical physics.

本文在局部分数阶导数理论的范围内，研究了(4+1)维局部分数阶Fokas方程。高维非线性偏微分方程精确解的研究对于理解现实中复杂的物理现象具有重要作用。本文分析了高维可积系统中定义在康托集上的广义函数的精确行波解。当分形维数等于 $\rho =ln2/ln3$ 时，对不同情况下不可微解的结果进行数值模拟。结果表明，局部分式Fokas方程的精确解代表了浅水面的分形波。通过数值模拟，我们发现局部分式Fokas方程的精确解可以描述浅水面的分形波和波浪特征。这也说明了非线性局部分式方程行波解的研究在数学物理中具有重要的意义。