The Two-Component Discrete KP Hierarchy

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2026-04-02 DOI:10.1111/sapm.70213

Wenqi Cao, Jipeng Cheng, Jinbiao Wang

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引用次数: 0

Abstract

The discrete KP hierarchy is also known as the $(l - l^{'})$ th modified KP hierarchy. In this paper, we consider the corresponding two-component generalization, known as the two-component discrete KP (2dKP) hierarchy. First, starting from the bilinear equation of the 2dKP hierarchy, we derive the corresponding Lax equation by the Shiota method, which uses scalar Lax operators involving two difference operators, $Λ_{1}$ and $Λ_{2}$ . Then, starting from the 2dKP Lax equation, we obtain the corresponding bilinear equation, which includes the existence of the tau function. From the above discussions, we can determine which are essential in the 2dKP Lax formulation. Finally, we discuss the reduction of the 2dKP hierarchy corresponding to the loop algebra ${\hat{s l}}_{M + N} = s l_{M + N} [λ, λ^{- 1}] \oplus C c (M, N \geq 1)$ .

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二元离散KP层次

离散KP层次也被称为（l−l '） $(l-l^{\prime })$修正KP层次。在本文中，我们考虑相应的双分量泛化，称为双分量离散KP （2dKP）层次。首先，从2dKP层次的双线性方程出发，利用涉及两个差分算子Λ 1 $\Lambda _1$和Λ 2 $\Lambda _2$的标量Lax算子，用Shiota方法推导出相应的Lax方程。然后，从2dKP Lax方程出发，得到相应的双线性方程，其中包含tau函数的存在性。从上面的讨论，我们可以确定哪些是必不可少的2dKP Lax公式。最后，讨论了对应于循环代数s l l M + N = s的2dKP层次的约简l M + N [λ，λ−1]⊕C C (M，N≥1)$\widehat{sl}_{M+N}=sl_{M+N}[\lambda,\lambda ^{-1}]\oplus \mathbb {C}c \ (M,N\ge 1)$。

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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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.