THERMAL SCIENCE

International Scientific Journal

Chu-Han Shang

,

Huai-An Yi

SOLUTIONS OF THE KDV-MKDV EQUATIONS ARISING IN NON-LINEAR ELASTIC RODS UNDER FRACTAL DIMENSION

ABSTRACT
A prediction of rod wave type with great precision is extremely important in theoretical analysis and practical applications. Besides the well-known periodic motion and resonance, this paper studies the rod wave in a fractal space, and a fractal solitary wave is unlocked by the variational approach, the results reveal that the rod strain non-linearity and fractal dimensions affect greatly the wave travelling properties. This paper offers a new window for identifying a solitary wave from periodic motion easily and accurately.
KEYWORDS
non-linear elastic rod, KdV-MKdV equation, He's fractal derivatives, He-Weierstrass function, soliton
PAPER SUBMITTED: 2022-11-09
PAPER REVISED: 2023-05-25
PAPER ACCEPTED: 2023-05-28
PUBLISHED ONLINE: 2024-05-18
DOI REFERENCE: https://doi.org/10.2298/TSCI2403125S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE No. 3, PAGES [2125 - 2133]
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Solutions of the KdV-MKdV equations arising in non-linear elastic rods under fractal dimension

© 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