From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910922530881536 |
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| author | Konstantinou-Rizos, Sotiris |
| author_facet | Konstantinou-Rizos, Sotiris |
| contents | We present a method for constructing hierarchies of solutions to $n$-simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex equations which are related to the Adler map and Nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang--Baxter maps are completely integrable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations Konstantinou-Rizos, Sotiris Exactly Solvable and Integrable Systems Mathematical Physics We present a method for constructing hierarchies of solutions to $n$-simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex equations which are related to the Adler map and Nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang--Baxter maps are completely integrable. |
| title | From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2504.21094 |