{"title":"Constructing degenerate lumped solutions for the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation","authors":"Mengru Xu, Biao Li","doi":"10.1140/epjp/s13360-025-06404-y","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(N\\)</span> 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.</p></div>","PeriodicalId":792,"journal":{"name":"The European Physical Journal Plus","volume":"140 5","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal Plus","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjp/s13360-025-06404-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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 \(N\) 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.
期刊介绍：
The aims of this peer-reviewed online journal are to distribute and archive all relevant material required to document, assess, validate and reconstruct in detail the body of knowledge in the physical and related sciences.
The scope of EPJ Plus encompasses a broad landscape of fields and disciplines in the physical and related sciences - such as covered by the topical EPJ journals and with the explicit addition of geophysics, astrophysics, general relativity and cosmology, mathematical and quantum physics, classical and fluid mechanics, accelerator and medical physics, as well as physics techniques applied to any other topics, including energy, environment and cultural heritage.
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