https://doi.org/10.1140/epjp/s13360-023-04774-9
Regular Article
Waves in motion: unraveling nonlinear behavior through the Gilson–Pickering equation
1
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, People’s Republic of China
2
Department of Basic Science, Obour High Institute for Engineering and Technology, 11828, Cairo, Egypt
a mostafa.khater2024@yahoo.com, Mostafa.khater2024@xzhmu.edu.cn
Received:
23
June
2023
Accepted:
3
December
2023
Published online:
19
December
2023
This study addresses the challenge of solving the nonlinear Gilson–Pickering 
equation, employing the unified method for analytical investigation and verifying the results through the He’s variational iteration method. The primary aim is to offer a robust solution for this complex equation. The research methodology integrates the unified method for analytical purposes and validates the outcomes through numerical approaches. The study’s significance lies in successfully resolving the 
equation, showcasing its applicability in various scientific contexts. This research’s implications are substantial, as it introduces an effective solution method with broad interdisciplinary relevance. In conclusion, the study underscores the compatibility of the proposed unified method with numerical solutions, contributing a novel perspective to mathematical modeling. This work pertains to the field of mathematical sciences and is theoretical, involving no specific subjects or participants.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
