Lax formulation of 3--component KP hierarchy by Shiota construction
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929444213489664 |
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| author | Cui, Tongtong Wang, Jinbiao Cao, Wenqi Cheng, Jipeng |
| author_facet | Cui, Tongtong Wang, Jinbiao Cao, Wenqi Cheng, Jipeng |
| contents | It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators $Λ_1$ and $Λ_2$, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lax formulation of 3--component KP hierarchy by Shiota construction Cui, Tongtong Wang, Jinbiao Cao, Wenqi Cheng, Jipeng Exactly Solvable and Integrable Systems Mathematical Physics 35Q53, 37K10, 35Q51 It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators $Λ_1$ and $Λ_2$, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases. |
| title | Lax formulation of 3--component KP hierarchy by Shiota construction |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35Q53, 37K10, 35Q51 |
| url | https://arxiv.org/abs/2407.21334 |