Residual Symmetry Reductions and Painlevé Solitons
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911449212780544 |
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| author | Li, Yan Xia, Ya-Rong Yao, Ruo-Xia Lou, S. Y. |
| author_facet | Li, Yan Xia, Ya-Rong Yao, Ruo-Xia Lou, S. Y. |
| contents | This letter introduces the novel concept of Painlevé solitons -- waves arising from the interaction between Painlevé waves and solitons in integrable systems. Painlevé solitons may also be viewed as solitons propagating against a Painlevé wave background, in analogy with the established notion of elliptic solitons, which refer to solitons on an elliptic wave background. By employing a novel symmetry decomposition method aided by nonlocal residual symmetries, we explicitly construct (extended) Painlevé II solitons for the Korteweg-de Vries (KdV) equation and (extended) Painlevé IV solitons for the Boussinesq equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Residual Symmetry Reductions and Painlevé Solitons Li, Yan Xia, Ya-Rong Yao, Ruo-Xia Lou, S. Y. Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons This letter introduces the novel concept of Painlevé solitons -- waves arising from the interaction between Painlevé waves and solitons in integrable systems. Painlevé solitons may also be viewed as solitons propagating against a Painlevé wave background, in analogy with the established notion of elliptic solitons, which refer to solitons on an elliptic wave background. By employing a novel symmetry decomposition method aided by nonlocal residual symmetries, we explicitly construct (extended) Painlevé II solitons for the Korteweg-de Vries (KdV) equation and (extended) Painlevé IV solitons for the Boussinesq equation. |
| title | Residual Symmetry Reductions and Painlevé Solitons |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2511.09077 |