{"title":"(2 + 1)维多分量阿布洛维茨-考普-纽维尔-塞古尔层次结构的积分分解及其应用","authors":"Xiaoming Zhu, Shiqing Mi","doi":"10.1063/5.0203907","DOIUrl":null,"url":null,"abstract":"This paper investigates integrable decompositions of the (2 + 1)-dimensional multi-component Ablowitz-Kaup-Newell-Segur (AKNS in brief) hierarchy. By utilizing recursive relations and symmetric reductions, it is demonstrated that the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional coupled multi-component AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the coupled multi-component AKNS hierarchy. Specifically, except for two specific scenarios, the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional reduced multi-component AKNS hierarchy can similarly be decomposed into the corresponding n1-flow and n2-flow of the reduced multi-component AKNS hierarchy. Through the application of these integrable decompositions and Darboux transformation techniques, multiple solitons for the standard focusing multi-component “breaking soliton” equations, as well as singular, exponential, and rational solitons for the nonlocal defocusing multi-component “breaking soliton” equations, are systematically presented. Furthermore, the elastic interactions and dynamical behaviors among these soliton solutions are thoroughly investigated without loss of generality.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integrable decompositions for the (2 + 1)-dimensional multi-component Ablowitz–Kaup–Newell–Segur hierarchy and their applications\",\"authors\":\"Xiaoming Zhu, Shiqing Mi\",\"doi\":\"10.1063/5.0203907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper investigates integrable decompositions of the (2 + 1)-dimensional multi-component Ablowitz-Kaup-Newell-Segur (AKNS in brief) hierarchy. By utilizing recursive relations and symmetric reductions, it is demonstrated that the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional coupled multi-component AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the coupled multi-component AKNS hierarchy. Specifically, except for two specific scenarios, the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional reduced multi-component AKNS hierarchy can similarly be decomposed into the corresponding n1-flow and n2-flow of the reduced multi-component AKNS hierarchy. Through the application of these integrable decompositions and Darboux transformation techniques, multiple solitons for the standard focusing multi-component “breaking soliton” equations, as well as singular, exponential, and rational solitons for the nonlocal defocusing multi-component “breaking soliton” equations, are systematically presented. Furthermore, the elastic interactions and dynamical behaviors among these soliton solutions are thoroughly investigated without loss of generality.\",\"PeriodicalId\":16174,\"journal\":{\"name\":\"Journal of Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0203907\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0203907","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Integrable decompositions for the (2 + 1)-dimensional multi-component Ablowitz–Kaup–Newell–Segur hierarchy and their applications
This paper investigates integrable decompositions of the (2 + 1)-dimensional multi-component Ablowitz-Kaup-Newell-Segur (AKNS in brief) hierarchy. By utilizing recursive relations and symmetric reductions, it is demonstrated that the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional coupled multi-component AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the coupled multi-component AKNS hierarchy. Specifically, except for two specific scenarios, the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional reduced multi-component AKNS hierarchy can similarly be decomposed into the corresponding n1-flow and n2-flow of the reduced multi-component AKNS hierarchy. Through the application of these integrable decompositions and Darboux transformation techniques, multiple solitons for the standard focusing multi-component “breaking soliton” equations, as well as singular, exponential, and rational solitons for the nonlocal defocusing multi-component “breaking soliton” equations, are systematically presented. Furthermore, the elastic interactions and dynamical behaviors among these soliton solutions are thoroughly investigated without loss of generality.
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