https://doi.org/10.1140/epjp/s13360-025-06513-8
Regular Article
Soliton-M-lump wave formation and other interacting propagation for the nonlinear Geng equation
1
Department of Mathematics, College of Science, University of Zakho, Zakho, Iraq
2
Department of Computer Science, College of Science, Knowledge University, 44001, Erbil, Iraq
3
Department of Mathematics, Firat University, Elazig, Turkey
4
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, 602105, Chennai, Tamil Nadu, India
5
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
6
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
7
Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan
Received:
17
October
2024
Accepted:
2
June
2025
Published online:
24
June
2025
In this work, we obtain various kind of lump interaction solutions for the (3 + 1)-dimensional nonlinear Geng equation, which was derived in relation to Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobian. The well-known technique namely Hirota bilinear is used to accomplish the task. A lump solution is a real analytical rational function solution that decays in all directions of the space variables. The governing equation describes wave dynamical behaviors in more complex applications related to shallow water wave or other similar fluids. Numerical simulations using the three-dimensional and contour profiles are carried out with careful consideration for the values of the involved parameters in order to shed more light on the properties of the acquired solutions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
