## THERMAL SCIENCE

International Scientific Journal

### A FRACTAL VARIATIONAL THEORY OF THE BROER-KAUP SYSTEM IN SHALLOW WATER WAVES

**ABSTRACT**

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**

PAPER SUBMITTED: 2018-05-10

PAPER REVISED: 2018-06-20

PAPER ACCEPTED: 2018-06-28

PUBLISHED ONLINE: 2021-03-27

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 3**, PAGES [2051 - 2056]

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