3属三角谱曲线对应的2阶可交换微分算子

IF 0.7 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI:10.1134/S1234567826010088

Matvey Ivlev

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引用次数: 0

摘要

普通可交换微分算子的构造是微分方程和可积系统中的一个经典问题，在孤子理论中有着广泛的应用。秩1的交换算子是由krichhever发现的。在一般情况下，构造秩为\(l>1\)的算子的问题还没有解决。在所有已知的秩为\(l>1\)的算符的例子中，光谱曲线都是超椭圆曲线。本文构造了3属三角谱曲线对应的2阶算子的第一个例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.