THERMAL SCIENCE

International Scientific Journal

Xiao-Qun Cao

,

Bai-Nian Liu

,

Meng-Zhu Liu

,

Ke-Cheng Peng

,

Wen-Long Tian

VARIATIONAL PRINCIPLES FOR TWO KINDS OF NON-LINEAR GEOPHYSICAL KDV EQUATION WITH FRACTAL DERIVATIVES

ABSTRACT
It is an important and difficult inverse problem to construct variational principles from complex models directly, because their variational formulations are theoretical bases for many methods to solve or analyze the non-linear problems. At first, this paper extends two kinds of non-linear geophysical KdV equations in continuum mechanics to their fractional partners in fractal porous media or with irregular boundaries. Then, by designing skillfully, the trial-Lagrange functional, variational principles are successfully established for the non-linear geophysical KdV equation with Coriolis term, and the high-order extended KdV equation with fractal derivatives, respectively. Furthermore, the obtained variational principles are proved to be correct by minimizing the functionals with the calculus of variations.
KEYWORDS
variational principle, geophysical KdV equation, fractal dimension, high-order extended KdV equation, semi-inverse method
PAPER SUBMITTED: 2020-10-04
PAPER REVISED: 2021-10-01
PAPER ACCEPTED: 2021-10-01
PUBLISHED ONLINE: 2022-07-16
DOI REFERENCE: https://doi.org/10.2298/TSCI2203505C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 3, PAGES [2505 - 2515]
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Variational principles for two kinds of non-linear geophysical KdV equation with fractal derivatives

© 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