D. A. Domanevsky, A. V. Zotov, “Classical integrable spin chains of Landau–Lifshitz type from <nobr>$R$</nobr>-matrix identities”, Pis'ma v Zh. Èksper. Teoret. Fiz., 2025, Volume 121, Issue 12,Pages <nobr>964

METHODS OF PHYSICAL INVESTIGATION

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

D. A. Domanevsky^a, A. V. Zotov^b

^a Lomonosov Moscow State University, Moscow, 119991 Russia
^b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991 Russia

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.

Received: 14.05.2025
Revised: 21.05.2025
Accepted: 22.05.2025

DOI: 10.31857/S0370274X25060173