晶格Gelfand-Dickey层次的扩展与推广

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED Mathematical Physics, Analysis and Geometry Pub Date : 2023-07-29 DOI:10.1007/s11040-023-09461-w

Lixiang Zhang, Chuanzhong Li

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引用次数: 0

摘要

本文对扩展格Gelfand-Dickey层次构造了它的n次Darboux变换和附加流。我们证明了这些流实际上是扩展晶格Gelfand-Dickey层次结构的对称性。此外，我们还展示了附加流如何作用于tau函数。在此基础上，我们将扩展格Gelfand-Dickey层次推广到多分量和非交换版本，并给出了这些版本的Lax方程、Sato方程、零曲率方程和其他等价表达式。此外，我们还研究了它们的达布变换和附加的对称性。

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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Extensions and Generalizations of Lattice Gelfand–Dickey Hierarchy

In this paper, for the extended lattice Gelfand–Dickey hierarchy, we construct its n-fold Darboux transformation and additional flows. And we prove that these flows are actually symmetries of the extended lattice Gelfand–Dickey hierarchy. Further, we show how the additional flows act on the tau function. On this basis, we generalize the extended lattice Gelfand–Dickey hierarchy to the multicomponent and noncommutative versions, and give the Lax equations, Sato equations, zero-curvature equations and other equivalent expressions of these versions. Moreover, we investigate their Darboux transformations and additional symmetries.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.