THERMAL SCIENCE

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Wei-Wei Ling

,

Pin-Xia Wu

VARIATIONAL THEORY FOR A KIND OF NON-LINEAR MODEL FOR WATER WAVES

ABSTRACT
The Whitham-Broer-Kaup equation exists widely in shallow water waves, but unsmooth boundary seriously affects the properties of solitary waves and has certain deviations in scientific research. The aim of this paper is to introduce its modification with fractal derivatives in a fractal space and to establish a fractal variational formulation by the semi-inverse method. The obtained fractal variational principle shows conservation laws in an energy form in the fractal space and also hints its possible solution structure.
KEYWORDS
The Whitham-Broer-Kaup Equation, Fractal derivatives, two-scale transform, fractal variational formulation
PAPER SUBMITTED: 2020-03-01
PAPER REVISED: 2020-06-15
PAPER ACCEPTED: 2020-06-15
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200301019L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1249 - 1254]
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Variational theory for a kind of non-linear model for water waves

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