In this work we study the two-dimensional local fractional Boussinesq equation. Based on the basic definitions and properties of the local fractional derivatives and bilinear form, we studied the soliton solutions of non-differentiable type with the generalized functions defined on Cantor sets by using bilinear method. Meanwhile, we discuss the result when fractal dimension is 1, and compare it with the result when fractal dimension is $\frac{ln2}{ln3}$.

中文翻译：

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二维局部分数阶Boussinesq方程的孤子解

在这项工作中，我们研究二维局部分数 Boussinesq 方程。基于局部分数阶导数和双线性形式的基本定义和性质，利用双线性方法研究了康托集上定义的广义函数的不可微型孤子解。同时我们讨论了分形维数为1时的结果，并与分形维数为1时的结果进行了比较。$\frac{因2}{因3}$。