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

2025/05/15 by Domanevsky, D., Zotov, A. · 2 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2505.09918

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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• Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain
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