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Abstract <p> The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications in soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l&gt;1\)</EquationSource> </InlineEquation> has not been solved in the general case. In all known examples of operators of rank <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(l&gt;1\)</EquationSource> </InlineEquation>, the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed. </p>

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On Commuting Differential Operators of Rank 2 Corresponding to Trigonal Spectral Curves of Genus 3

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Matvey Ivlev

摘要

Abstract

The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications in soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank \(l>1\) has not been solved in the general case. In all known examples of operators of rank \(l>1\) , the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed.