Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices
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| Format: | Preprint |
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2025
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| _version_ | 1866909447108952064 |
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| author | Adamopoulou, P. Kouloukas, T. E. Papamikos, G. |
| author_facet | Adamopoulou, P. Kouloukas, T. E. Papamikos, G. |
| contents | We generalise a family of quadrirational parametric Yang-Baxter maps with $3\times 3$ Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational Yang-Baxter maps, and we discuss some of their integrability properties. This work is part of a more general classification of Yang-Baxter maps admitting a strong $3\times 3$ Lax matrix with a linear dependence on the spectral parameter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices Adamopoulou, P. Kouloukas, T. E. Papamikos, G. Exactly Solvable and Integrable Systems Mathematical Physics We generalise a family of quadrirational parametric Yang-Baxter maps with $3\times 3$ Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational Yang-Baxter maps, and we discuss some of their integrability properties. This work is part of a more general classification of Yang-Baxter maps admitting a strong $3\times 3$ Lax matrix with a linear dependence on the spectral parameter. |
| title | Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2501.01210 |