Prolongation Structure of a Development Equation and Its Darboux Transformation Solution
This paper explores the third-order nonlinear coupled KdV equation utilizing prolongation structure theory and gauge transformation. By applying the prolongation structure method, we obtained an extended version of the equation. Starting from the Lax pairs of the equation, we successfully derived th...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/6/921 |
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| _version_ | 1849342622662918144 |
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| author | Lixiu Wang Jihong Wang Yangjie Jia |
| author_facet | Lixiu Wang Jihong Wang Yangjie Jia |
| author_sort | Lixiu Wang |
| collection | DOAJ |
| description | This paper explores the third-order nonlinear coupled KdV equation utilizing prolongation structure theory and gauge transformation. By applying the prolongation structure method, we obtained an extended version of the equation. Starting from the Lax pairs of the equation, we successfully derived the corresponding Darboux transformation and Bäcklund transformation for this equation, which are fundamental to our solving process. Subsequently, we constructed and calculated the recursive operator for this equation, providing an effective approach to tackling complex problems within this domain. These results are crucial for advancing our understanding of the underlying principles of soliton theory and their implications on related natural phenomena. Our findings not only enrich the theoretical framework but also offer practical tools for further research in nonlinear wave dynamics. |
| format | Article |
| id | doaj-art-6ae6234e9a7b474c9f15c5d0e9ff8c72 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6ae6234e9a7b474c9f15c5d0e9ff8c722025-08-20T03:43:20ZengMDPI AGMathematics2227-73902025-03-0113692110.3390/math13060921Prolongation Structure of a Development Equation and Its Darboux Transformation SolutionLixiu Wang0Jihong Wang1Yangjie Jia2School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, ChinaSchool of Mathematics and Statistics, Qinghai Normal University, Xining 810008, ChinaSchool of Mathematics and Statistics, Qinghai Normal University, Xining 810008, ChinaThis paper explores the third-order nonlinear coupled KdV equation utilizing prolongation structure theory and gauge transformation. By applying the prolongation structure method, we obtained an extended version of the equation. Starting from the Lax pairs of the equation, we successfully derived the corresponding Darboux transformation and Bäcklund transformation for this equation, which are fundamental to our solving process. Subsequently, we constructed and calculated the recursive operator for this equation, providing an effective approach to tackling complex problems within this domain. These results are crucial for advancing our understanding of the underlying principles of soliton theory and their implications on related natural phenomena. Our findings not only enrich the theoretical framework but also offer practical tools for further research in nonlinear wave dynamics.https://www.mdpi.com/2227-7390/13/6/921recursive operatorBäcklund transformationDarboux transformationLax pairprolongation structure |
| spellingShingle | Lixiu Wang Jihong Wang Yangjie Jia Prolongation Structure of a Development Equation and Its Darboux Transformation Solution Mathematics recursive operator Bäcklund transformation Darboux transformation Lax pair prolongation structure |
| title | Prolongation Structure of a Development Equation and Its Darboux Transformation Solution |
| title_full | Prolongation Structure of a Development Equation and Its Darboux Transformation Solution |
| title_fullStr | Prolongation Structure of a Development Equation and Its Darboux Transformation Solution |
| title_full_unstemmed | Prolongation Structure of a Development Equation and Its Darboux Transformation Solution |
| title_short | Prolongation Structure of a Development Equation and Its Darboux Transformation Solution |
| title_sort | prolongation structure of a development equation and its darboux transformation solution |
| topic | recursive operator Bäcklund transformation Darboux transformation Lax pair prolongation structure |
| url | https://www.mdpi.com/2227-7390/13/6/921 |
| work_keys_str_mv | AT lixiuwang prolongationstructureofadevelopmentequationanditsdarbouxtransformationsolution AT jihongwang prolongationstructureofadevelopmentequationanditsdarbouxtransformationsolution AT yangjiejia prolongationstructureofadevelopmentequationanditsdarbouxtransformationsolution |