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THERMAL SCIENCE
International Scientific Journal
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FRACTAL SOLITARY WAVE SOLUTIONS AND VARIATIONAL PRINCIPLE OF THE FRACTAL GENERAL KADOMTSEV-PETVIASHVILI EQUATION
ABSTRACT
This work examines the fractal generalized Kadomtsev-Petviashvili equation, which describes the evolution of non-linear long waves of small amplitude. The fractal traveling wave transformation and the fractal semi-inverse method are employed to derive a fractal variational principle, which was found to be a strong minimum according to the He-Weierstrass function. The solution of the two examples is presented in the form of images. This paper demonstrates that the fractal dimension affects the waveform of the generalized Kadomtsev-Petviashvili equation.
KEYWORDS
He’s fractal derivatives, fractal variational principle, semi-inverse method, He-Weierstrass function, fractal solitary wave solutions
PAPER SUBMITTED: 2023-08-11
PAPER REVISED: 2024-02-23
PAPER ACCEPTED: 2024-03-01
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503775S
CITATION EXPORT: view in browser or download as text file
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© 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