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arXiv · 2505.09918

Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities

D. Domanevsky·A. Zotov
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Abstract

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.

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D. Domanevsky, A. Zotov. 2025-05-15. Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities. https://doi.org/10.1134/s0021364025606967

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