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<p>We describe a family of 1+1 classical integrable space-discrete models of the Landau–Lifshitz type through the usage of ansatz for <i>U</i>–<i>V</i> (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov–Shabat equation. The ansatz for <i>U</i>–<i>V</i> pair is based on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4209_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\)</EquationSource> <!--JETPLet2560696Zotov-m1--> </InlineEquation>-matrices satisfying the associative Yang–Baxter equation and certain additional properties. Equations of motion are obtained using a set of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4209_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\)</EquationSource> <!--JETPLet2560696Zotov-m2--> </InlineEquation>-matrix identities. In the continuous limit we reproduce the previously known family of the higher rank Landau–Lifshitz equations.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年6月10日

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  • D. Domanevsky,
  • A. Zotov

摘要

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.