约化齐次空间上Mikhailov-Lenells系统的几何实现 \(GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3\)

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-05-16 DOI:10.1007/s13324-025-01075-5

Shiping Zhong, Zehui Zhao, Jinhuan Wang

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引用次数: 0

摘要

本文利用Yang-Mills理论框架下的零曲率表示，探讨了由两个线性\(3\times 3\)矩阵谱问题的Lax对构造的Mikhailov-Lenells系统的几何性质。在初始数据适当限制的情况下，在约化齐次空间\(GL(3,\mathbb C)/({\mathbb {C}}^*)^3\)中演化的Sym-Pohlmeyer运动曲线的Landau-Lifshitz型模型与Mikhailov-Lenells系统规范等效。这给出了米哈伊洛夫-莱内尔系统的几何实现。

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Geometric realization of the Mikhailov-Lenells system on the reductive homogeneous space \(GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3\)

Using the zero curvature representation within the framework of Yang-Mills theory, this paper is devoted to exploring geometric properties of the Mikhailov-Lenells system, which was constructed from Lax pairs of two linear \(3\times 3\) matrix spectral problems. The Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space \(GL(3,\mathbb C)/({\mathbb {C}}^*)^3\) with initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.