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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/2601.20277 |
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| _version_ | 1866910003245350912 |
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| author | Yuan, Feng He, Jingsong Cheng, Yi |
| author_facet | Yuan, Feng He, Jingsong Cheng, Yi |
| contents | The stem structure is a localized feature that arises during high-order soliton interactions, connecting the vertices of two V-shaped waveforms. The interaction of resonant 3-solitons is accompanied by soliton reconnection phenomena, characterized by the disappearance and reconnection of stem structures. This paper investigates variable-length stem structures in resonant 3-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation, focusing on both 2-resonant and 3-resonant 3-soliton cases. Depending on the phase shift tends to plus/minus infinity, different types of resonances are identified, including strong resonance, weak resonance, and mixed (strong-weak) resonance. We derive and analyze the asymptotic forms and explicit expressions for the soliton arm trajectories, velocities, as well as the endpoints, length, and amplitude of the stem structures. A detailed comparison is made between the similarities and differences of the stem structures in the 2-resonant and 3-resonant solitons. In addition, we provide a comprehensive and rigorous analysis of both the asymptotic behavior and the structural properties of the stems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The variable-length stem structures in three-soliton resonance of the Kadomtsev-Petviashvili II equation Yuan, Feng He, Jingsong Cheng, Yi Mathematical Physics The stem structure is a localized feature that arises during high-order soliton interactions, connecting the vertices of two V-shaped waveforms. The interaction of resonant 3-solitons is accompanied by soliton reconnection phenomena, characterized by the disappearance and reconnection of stem structures. This paper investigates variable-length stem structures in resonant 3-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation, focusing on both 2-resonant and 3-resonant 3-soliton cases. Depending on the phase shift tends to plus/minus infinity, different types of resonances are identified, including strong resonance, weak resonance, and mixed (strong-weak) resonance. We derive and analyze the asymptotic forms and explicit expressions for the soliton arm trajectories, velocities, as well as the endpoints, length, and amplitude of the stem structures. A detailed comparison is made between the similarities and differences of the stem structures in the 2-resonant and 3-resonant solitons. In addition, we provide a comprehensive and rigorous analysis of both the asymptotic behavior and the structural properties of the stems. |
| title | The variable-length stem structures in three-soliton resonance of the Kadomtsev-Petviashvili II equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.20277 |