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Abstract <p> We present a method for constructing hierarchies of solutions of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2658_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation>-simplex equations by varying the spectral parameter in their Lax representation. We use this method to derive new solutions of the set-theoretic <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2658_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\)</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2658_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> </InlineEquation>-simplex equations that are related to the Adler map and nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang–Baxter maps are completely integrable. </p>

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From NLS-type matrix refactorization problems to set-theoretic solutions of the 2- and 3-simplex equations

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • S. Konstantinou-Rizos

摘要

Abstract

We present a method for constructing hierarchies of solutions of \(n\) -simplex equations by varying the spectral parameter in their Lax representation. We use this method to derive new solutions of the set-theoretic \(2\) - and \(3\) -simplex equations that are related to the Adler map and nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang–Baxter maps are completely integrable.