{"title":"Dynamic properties of soliton solutions for the generalized KDKK and BK equations","authors":"Deniu Yang","doi":"10.1140/epjp/s13360-025-06218-y","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this paper is to study dynamic properties of soliton solutions for the generalized KDKK and BK equations. The bilinear form and N-soliton are obtained using the Hirota bilinear method. Under the condition <span>\\(a_{ij}=0\\)</span>, <span>\\(a_{ij}={{\\infty }}\\)</span>, <span>\\(a_{ij}\\approx 0\\)</span> or <span>\\(a_{ij}={{\\infty }}\\)</span>, the resonant collision between two solitons, three solitons are analyzed in detail, respectively. The X-shaped, double X-shaped, and Y-shaped solitons are obtained. For the complex conjugate parameters, the interaction between a solitary and a breather is discussed via their phase shifts. In particular, the process of the interaction is analyzed, and the phenomena of fusion and fission which have important physical significance are discovered. The asymptotic interaction behavior of these solutions is analyzed theoretically and demonstrated visually by plots.</p></div>","PeriodicalId":792,"journal":{"name":"The European Physical Journal Plus","volume":"140 3","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjp/s13360-025-06218-y.pdf","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/s13360-025-06218-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}
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Abstract
The purpose of this paper is to study dynamic properties of soliton solutions for the generalized KDKK and BK equations. The bilinear form and N-soliton are obtained using the Hirota bilinear method. Under the condition \(a_{ij}=0\), \(a_{ij}={{\infty }}\), \(a_{ij}\approx 0\) or \(a_{ij}={{\infty }}\), the resonant collision between two solitons, three solitons are analyzed in detail, respectively. The X-shaped, double X-shaped, and Y-shaped solitons are obtained. For the complex conjugate parameters, the interaction between a solitary and a breather is discussed via their phase shifts. In particular, the process of the interaction is analyzed, and the phenomena of fusion and fission which have important physical significance are discovered. The asymptotic interaction behavior of these solutions is analyzed theoretically and demonstrated visually by plots.
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