Soliton,breathers,positons and rogue waves for the vector complex modified Korteweg-de Vries equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915531932565504 |
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| author | Liu, Yihang Zhang, Yongshuai Li, Maohua |
| author_facet | Liu, Yihang Zhang, Yongshuai Li, Maohua |
| contents | This paper constructs the $N$-fold Darboux transformation (DT) for the vector complex modified Korteweg-de Vries (vcmKdV) equation and presents its determinant representation. Utilizing the DT and multi-fold eigenvalue degeneracy, we derive globally bounded solutions for the vcmKdV equation, including $N$-bright-bright-bright solitons, $N$-dark-bright-bright solitons, $N$-breathers, $N$-positon solutions, and $N$th-order rogue wave solutions." All these solutions are globally bounded. Graphical representations of bright-bright-bright and dark-bright-bright soliton solutions are provided, illustrating phenomena where periodic oscillatory waves coexist or interact with solitons. The collision scenarios of the two-bright-bright-bright solution have been investigated by using the asymptotic analysis. The bounded Akhmediev breather, the bounded breather with dark-bright soliton and breather-breather mixed waves are graphically shown. We give the graphs of the positon solution, the rogue wave and the rogue wave mixes with dark-bright solitons and breathers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soliton,breathers,positons and rogue waves for the vector complex modified Korteweg-de Vries equation Liu, Yihang Zhang, Yongshuai Li, Maohua Exactly Solvable and Integrable Systems This paper constructs the $N$-fold Darboux transformation (DT) for the vector complex modified Korteweg-de Vries (vcmKdV) equation and presents its determinant representation. Utilizing the DT and multi-fold eigenvalue degeneracy, we derive globally bounded solutions for the vcmKdV equation, including $N$-bright-bright-bright solitons, $N$-dark-bright-bright solitons, $N$-breathers, $N$-positon solutions, and $N$th-order rogue wave solutions." All these solutions are globally bounded. Graphical representations of bright-bright-bright and dark-bright-bright soliton solutions are provided, illustrating phenomena where periodic oscillatory waves coexist or interact with solitons. The collision scenarios of the two-bright-bright-bright solution have been investigated by using the asymptotic analysis. The bounded Akhmediev breather, the bounded breather with dark-bright soliton and breather-breather mixed waves are graphically shown. We give the graphs of the positon solution, the rogue wave and the rogue wave mixes with dark-bright solitons and breathers. |
| title | Soliton,breathers,positons and rogue waves for the vector complex modified Korteweg-de Vries equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.03062 |