Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908575847153664 |
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| author | Huang, Shilong Kodama, Yuji Li, Chuanzhong |
| author_facet | Huang, Shilong Kodama, Yuji Li, Chuanzhong |
| contents | We give a classification of the $regular$ soliton solutions of the KP hierarchy, referred to as the $KP solitons$, under the Gel'fand-Dickey $\ell$-reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have $at ~most$ one resonant soliton in addition to two sets of solitons propagating in opposite directions. We also give a systematic construction of these soliton solutions for the $\ell$-reductions using the vertex operators. In particular, we show that the $non-crossing$ permutation gives the regularity condition for the soliton solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators Huang, Shilong Kodama, Yuji Li, Chuanzhong Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics We give a classification of the $regular$ soliton solutions of the KP hierarchy, referred to as the $KP solitons$, under the Gel'fand-Dickey $\ell$-reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have $at ~most$ one resonant soliton in addition to two sets of solitons propagating in opposite directions. We also give a systematic construction of these soliton solutions for the $\ell$-reductions using the vertex operators. In particular, we show that the $non-crossing$ permutation gives the regularity condition for the soliton solutions. |
| title | Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2407.01900 |