Integrable Hierarchy for Homogeneous Realization of the Toroidal Lie Algebra L r + 1 tor ( sl ℓ ) $\mathcal {L}^{\mathrm{tor}}_{r+1}(\mathfrak {sl}_\ell)$

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-02-07 DOI:10.1111/sapm.70021

Chao-Zhong Wu, Yi Yang

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引用次数: 0

Abstract

Starting from a fairly explicit homogeneous realization of the toroidal Lie algebra $L_{r + 1}^{tor} ({sl}_{ℓ})$ via a lattice vertex algebra, we derive an integrable hierarchy of Hirota bilinear equations. Moreover, we represent this hierarchy in the form of Lax equations, and show that it is an extension of a certain reduction of the $ℓ$ -component KP hierarchy.

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从环面李代数 L r + 1 tor ( sl ℓ ) $\mathcal {L}^{mathrm{tor}}_{r+1}(\mathfrak {sl}_\ell)$ 通过晶格顶点代数的相当明确的同质实现出发，我们导出了广塔双线性方程的可积分层次。此外，我们用拉克斯方程的形式来表示这个层次结构，并证明它是ℓ $\ell$ -分量 KP 层次结构的某种还原的扩展。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.