Thermal Science

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Jianshe Sun

VARIATIONAL PRINCIPLE FOR FRACTAL HIGH-ORDER LONG WATER-WAVE EQUATION

ABSTRACT

In this article, we mainly consider a modification of the high-order long water-wave equation with unsmooth boundaries by adopting a new fractal derivative. Its fractal variational principles are successfully constructed by the fractal semi-inverse method, the obtained principles are helpful to study the symmetry, to discover the conserved quantity, and to have wide applications in numerical simulation.

KEYWORDS

variational principle, fractal semi-inverse method, fractal derivative, long water-wave equation

PAPER SUBMITTED: 2021-08-16

PAPER REVISED: 2022-07-15

PAPER ACCEPTED: 2022-07-15

PUBLISHED ONLINE: 2023-06-11

DOI REFERENCE: https://doi.org/10.2298/TSCI2303899S

CITATION EXPORT: view in browser or download as text file

THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE No. 3, PAGES [1899 - 1905]

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Variational principle for fractal high-order long water-wave equation

© 2026 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