{"title":"Conservation Laws, Darboux Transformation and Soliton Solutions of a Negative Order Generalized Ablowitz-Kaup-Newell-Segur System","authors":"Chen-Di Zhu, Jing Kang, Long-Xing Li","doi":"10.1007/s10773-025-05917-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we derive a new negative order generalized Ablowitz-Kaup-Newell-Segur system associated with a <span>\\(4 \\times 4\\)</span> matrix spectral problem. The infinitely many conservation laws and Hamiltonian structures of this system are constructed. The Darboux transformation of the negative order generalized Ablowitz-Kaup-Newell-Segur system is established and some multi-soliton solutions expressed by quasi-determinants are given. It is remarkable that two-solitons exhibit scattering with both phase shifts and amplitude changes. As a reduction, the Darboux transformation of two reduced systems and their soliton solutions including single-hump and double-hump solitons are obtained.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-025-05917-7","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we derive a new negative order generalized Ablowitz-Kaup-Newell-Segur system associated with a \(4 \times 4\) matrix spectral problem. The infinitely many conservation laws and Hamiltonian structures of this system are constructed. The Darboux transformation of the negative order generalized Ablowitz-Kaup-Newell-Segur system is established and some multi-soliton solutions expressed by quasi-determinants are given. It is remarkable that two-solitons exhibit scattering with both phase shifts and amplitude changes. As a reduction, the Darboux transformation of two reduced systems and their soliton solutions including single-hump and double-hump solitons are obtained.
期刊介绍：
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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