Linear integral equations and two-dimensional Toda systems
Linear integral equations and two-dimensional Toda systems
复制标题
线性积分方程和二维 Toda 系统
DOI：
10.1111/sapm.12427
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发表时间：
2021
影响因子：
2.7
通讯作者：
Wei Fu
中科院分区：
文献类型：
--
作者：
Yue Yin;Wei Fu
从某种形式的线性积分方程组的角度，提出了与无限维李代数 、 、 和 相关的二维 (2D) Toda 方程以及任意整数 的 Kac-Moody 代数 、 、 和 的直接线性化框架。这样的方案不仅提供了一个统一的视角来理解底层的可积性结构，而且还为 2D Toda 系统的每一类引入了可能导致通用解空间的直接线性化类型解。作为该框架在 2D Toda 格中的具体应用，我们重新发现了 Lax 对和伴随 Lax 对，并同时构造了广义柯西矩阵解。
The direct linearization framework is presented for the two‐dimensional (2D) Toda equations associated with the infinite‐dimensional Lie algebras , , and , as well as the Kac–Moody algebras , , , and for arbitrary integers , from the aspect of a set of linear integral equations in a certain form. Such a scheme not only provides a unified perspective to understand the underlying integrability structure, but also induces the direct linearizing type solution potentially leading to the universal solution space, for each class of the 2D Toda system. As particular applications of this framework to the 2D Toda lattices, we rediscover the Lax pairs and the adjoint Lax pairs and simultaneously construct the generalized Cauchy matrix solutions.