https://doi.org/10.1140/epjp/s13360-023-04063-5
Regular Article
Bäcklund transformation, Wronskian solutions and interaction solutions to the (3+1)-dimensional generalized breaking soliton equation
1
Department of Mathematics, Beijing Jiaotong University, 100044, Beijing, China
2
Beijing Laboratory of National Economic Security Early-warning Engineering, Beijing Jiaotong University, 100044, Beijing, China
3
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), 250353, Jinan, China
Received:
19
July
2022
Accepted:
2
May
2023
Published online:
4
June
2023
We focus on the (3+1)-dimensional generalized breaking soliton (GBS) equation, which describes a Riemann wave propagating along three spatial dimensions. The Wronskian solutions are derived for the (3+1)-dimensional GBS equation based on the Plücker relation for determinants. The lump-soliton solutions are generated by virtue of the test function method. Through the Bäcklund transformation (BT), we obtain various solutions via specifically choosing different seed solutions, including the Wronskian solutions and the interaction solutions. The relation between the Wronskian solutions and interaction solutions is established based on BT. The study of the (3+1)-dimensional GBS equation provides theoretical guidance for solving equations and increases the diversity of exact 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 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.
