https://doi.org/10.1140/epjp/s13360-025-06404-y
Regular Article
Constructing degenerate lumped solutions for the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation
School of Mathematics and Statistics, Ningbo University, 315211, Ningbo, People’s Republic of China
Received:
26
October
2024
Accepted:
6
May
2025
Published online:
26
May
2025
By applying Hirota’s bilinear method alongside a novel limiting approach, it is possible to derive degenerate lump solutions that encompass both the anomalous scattering of lumps and the weak interactions among multiple lumps from the 
soliton solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili equation. Improvements to the traditional limiting methods allow the anomalous scattering of two lumps to be obtained, as well as the asymptotic behavior of the anomalously scattering lumps to be discussed and investigated in detail. In addition, the study derives weak interactions among multiple lumps exhibiting intriguing patterns, such as triangles and quadrilaterals. The dynamic behaviors of these two weak interactions are also analyzed. Furthermore, the interactions between lumps and anomalous scattering lumps are investigated. These unique degenerate lump solutions contribute to a deeper understanding of the characteristics of lumps.
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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.
