Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
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| Format: | Preprint |
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2025
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| _version_ | 1866909695852150784 |
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| author | Domanevsky, D. Zotov, A. |
| author_facet | Domanevsky, D. Zotov, A. |
| contents | We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known family of the higher rank Landau-Lifshitz equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities Domanevsky, D. Zotov, A. Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known family of the higher rank Landau-Lifshitz equations. |
| title | Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.09918 |