In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg-de Vries-type (KdV-type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.

中文翻译：

---

与离散 Korteweg-de Vries 型方程相关的可积辛映射

在本文中，我们提出了与常微分方程相关的新的可积辛映射，并展示了它们如何以非常不同的方式确定可积偏微分方程的可积性，包括 Lax 对和显式解，这些偏微分方程是Korteweg-de Vries 型（KdV 型）的可积偏微分方程。因此，通过 Liouville 可积性框架证明了几个不同的哈密顿系统会导致一个相同的差分方程。因此，这些可积辛映射可以提供用于表征和确定偏差分方程的可积性的有效工具。