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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.23684 |
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| _version_ | 1866910270004133888 |
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| author | Wang, Yanan Zhang, Minghe |
| author_facet | Wang, Yanan Zhang, Minghe |
| contents | In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we construct the determinant form of the generalized Darboux transformation (DT). Secondly, we obtain deformed solitons, deformed positons on the zero background and deformed breathers, deformed Y-shaped breathers on the nonzero backgrounds by DT method. Finally, the undeformed solutions including higher-order rogue wave solutions and breather-rogue wave solutions are derived by generalized DT. This work enriches the solution family associated with the equation, but also illustrates the efficiency of DT method in multi-dimensional and multi-component systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23684 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformed and undeformed localized wave solutions for the two-component (2+1)-dimensional Fokas-Lenells equation Wang, Yanan Zhang, Minghe Mathematical Physics In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we construct the determinant form of the generalized Darboux transformation (DT). Secondly, we obtain deformed solitons, deformed positons on the zero background and deformed breathers, deformed Y-shaped breathers on the nonzero backgrounds by DT method. Finally, the undeformed solutions including higher-order rogue wave solutions and breather-rogue wave solutions are derived by generalized DT. This work enriches the solution family associated with the equation, but also illustrates the efficiency of DT method in multi-dimensional and multi-component systems. |
| title | Deformed and undeformed localized wave solutions for the two-component (2+1)-dimensional Fokas-Lenells equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2604.23684 |