https://doi.org/10.1140/epjp/s13360-024-05266-0
Regular Article
Lax integrability and infinite superposition solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation
1
College of Mathematics Science, Inner Mongolia Normal University, 010022, Huhhot, People’s Republic of China
2
Center for Applied Mathematics Inner Mongolia, 010022, Huhhot, People’s Republic of China
3
Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, 010022, Huhhot, People’s Republic of China
Received:
25
October
2023
Accepted:
11
May
2024
Published online:
2
June
2024
In this article, a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is studied, which is an extended shallow water wave model in the higher dimensions. Firstly, the bilinear form of the equation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws are derived using the symbolic calculation system and Bell polynomial method, and it is proved that the equation is completely integrable in the sense of Lax pair. Secondly, the nonlinear superposition formula of the equation is constructed using the obtained bilinear Bäcklund transformation, and some infinite superposition soliton solutions of the equation are also constructed based on the nonlinear superposition formula. Finally, based on the obtained bilinear equation, infinite superposition solutions of different types of functions are constructed, and the solutions images are drawn to analyze their dynamic characteristics. It is worth mentioning that this paper not only obtains a large number of properties based on the Bell polynomial method, but also derives infinite linear superposition solutions and nonlinear superposition solutions of the equation, making the solutions more diverse and diverse. These contents have not been studied in previous literatures.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
