The morphology of a shallow-water wave is affected by the unsmooth boundary, while its peak is rarely changed. This phenomenon cannot be explained by a differential model. This paper adopts a fractal modification of the Boussinesq equation, and its traveling solitary solution is studied through its fractal variational principle, the results reveal the basic properties of solitary waves in fractal space.

中文翻译：

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分形孤波的变分方法

浅水波的形态受不光滑边界的影响，而其波峰很少改变。这种现象不能用微分模型来解释。本文采用Boussinesq方程的分形修正，通过其分形变分原理研究其行孤解，结果揭示了分形空间中孤波的基本性质。