Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation
This paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The...
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023442?viewType=HTML |
| _version_ | 1811161959389724672 |
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| author | Qiulan Zhao Muhammad Arham Amin Xinyue Li |
| author_facet | Qiulan Zhao Muhammad Arham Amin Xinyue Li |
| author_sort | Qiulan Zhao |
| collection | DOAJ |
| description | This paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The classical Darboux transformation (DT) is utilized to construct multi-soliton solutions for the two-component c-SP equation as an ordinary determinant. Furthermore, the details of one-soliton and two-soliton solutions are presented and generalized for N-fold soliton solutions. We also derive exact soliton solutions in explicit form using suitable reduction constraints from various "seed" solutions and explore them via graphs. |
| first_indexed | 2024-04-10T06:22:23Z |
| format | Article |
| id | doaj.art-0fe1cb1a4add4b06ba5ab31b6b829e69 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T06:22:23Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0fe1cb1a4add4b06ba5ab31b6b829e692023-03-02T01:11:15ZengAIMS PressAIMS Mathematics2473-69882023-02-01848811882810.3934/math.2023442Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equationQiulan Zhao 0Muhammad Arham Amin 1Xinyue Li2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaThis paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The classical Darboux transformation (DT) is utilized to construct multi-soliton solutions for the two-component c-SP equation as an ordinary determinant. Furthermore, the details of one-soliton and two-soliton solutions are presented and generalized for N-fold soliton solutions. We also derive exact soliton solutions in explicit form using suitable reduction constraints from various "seed" solutions and explore them via graphs.https://www.aimspress.com/article/doi/10.3934/math.2023442?viewType=HTMLintegrabilityhodograph transformationdarboux transformationexact soliton solutions |
| spellingShingle | Qiulan Zhao Muhammad Arham Amin Xinyue Li Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation AIMS Mathematics integrability hodograph transformation darboux transformation exact soliton solutions |
| title | Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation |
| title_full | Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation |
| title_fullStr | Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation |
| title_full_unstemmed | Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation |
| title_short | Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation |
| title_sort | classical darboux transformation and exact soliton solutions of a two component complex short pulse equation |
| topic | integrability hodograph transformation darboux transformation exact soliton solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023442?viewType=HTML |
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