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arXiv:2505.09918 · Journal of Experimental and Theoretical Physics Letters

Classical Integrable Spin Chains of Landau–Lifshitz Type from R-Matrix Identities

D. Domanevsky, Andrei Vladimirovich Zotov

Published Jun 1, 2025• 2 citations
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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.

DOI
10.1134/s0021364025606967

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