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A fractal variational theory of the Broer-Kaup system in shallow water waves

Ling Wei-Wei (College of Social Management, Jiangxi College of Applied Technology, Ganzhou, Jiangxi, China), pinxiawu@csu.edu.cn
Wu Pin-Xia (School of Mathematics and Statistics, Central South University, Changsha, Hunan, China)

The Broer-Kaup equation is one of many equations describing some phenomena of shallow water wave. There are many errors in scientific research because of the existence of the non-smooth boundaries. In this paper, we generalize the Broer-Kaup equation to the fractal space and establish fractal variational formulations through the semi-inverse method. The acquired fractal variational formulation reveals conservation laws in an energy form in the fractal space and suggests possible solution structures of the morphology of the solitary waves

Keywords: Broer-Kaup equation, He’s fractal derivatives, two-scale transform, fractal variational formulation