Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas-Lenells equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912340198293504 |
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| author | Müller-Hoissen, Folkert Ye, Rusuo |
| author_facet | Müller-Hoissen, Folkert Ye, Rusuo |
| contents | Using a general result of bidifferential calculus and recent results of other authors, a vectorial binary Darboux transformation is derived for the first member of the "negative" part of the potential Kaup-Newell hierarchy, which is a system of two coupled Fokas-Lenells equations. Miura transformations are found from the latter to the first member of the negative part of the AKNS hierarchy and also to its "pseudodual". The reduction to the Fokas-Lenells equation is implemented and exact solutions with a plane wave seed generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas-Lenells equation Müller-Hoissen, Folkert Ye, Rusuo Exactly Solvable and Integrable Systems Mathematical Physics 35C08, 35Q51 Using a general result of bidifferential calculus and recent results of other authors, a vectorial binary Darboux transformation is derived for the first member of the "negative" part of the potential Kaup-Newell hierarchy, which is a system of two coupled Fokas-Lenells equations. Miura transformations are found from the latter to the first member of the negative part of the AKNS hierarchy and also to its "pseudodual". The reduction to the Fokas-Lenells equation is implemented and exact solutions with a plane wave seed generated. |
| title | Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas-Lenells equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35C08, 35Q51 |
| url | https://arxiv.org/abs/2504.12822 |