THERMAL SCIENCE

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Wei-Wei Ling

,

Pin-Xia Wu

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
TheBroer-Kaup equation(BK equation), He’s fractal derivatives, two-scale transform, fractal variational formulation
PAPER SUBMITTED: 2018-05-10
PAPER REVISED: 2018-06-20
PAPER ACCEPTED: 2018-06-28
PUBLISHED ONLINE: 2021-03-27
DOI REFERENCE: https://doi.org/10.2298/TSCI180510087L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2051 - 2056]
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A fractal variational theory of the Broer-Kaup system in shallow water waves

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence