对称离散 AKP 系统与双线性 ABS 网格方程之间的联系

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-12-25 DOI:arxiv-2312.15669

Jing Wang, Da-jun Zhang, Ken-ichi Maruno

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引用次数: 0

摘要

本文证明了所有双线性 Adler-Bobenko-Suris （ABS）方程（Q2 和 Q4 除外）都可以通过适当的还原和连续极限从对称离散 AKP 系统中得到。在双线性 ABS 方程中，给出了 ABS H2 方程更简单的双线性形式。此外，还得到了一个 8 点三维网格方程和一个 8 点四维网格方程作为副产品。这两个方程都可以看作是对称离散 AKP 方程的扩展。

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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Connection between the symmetric discrete AKP system and bilinear ABS lattice equations

In this paper, we show that all the bilinear Adler-Bobenko-Suris (ABS) equations (except Q2 and Q4) can be obtained from symmetric discrete AKP system by taking proper reductions and continuum limits. Among the bilinear ABS equations, a simpler bilinear form of the ABS H2 equation is given. In addition, an 8-point 3-dimensional lattice equation and an 8-point 4-dimensional lattice equation are obtained as by-products. Both of them can be considered as extensions of the symmetric discrete AKP equation.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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