Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on , which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other equations, including a second-degree second-order partial difference equation, which provide an unusual embedding into a three-dimensional lattice. The consistency of the resulting system extends a property that has been widely used to study partial difference equations on multidimensional lattices.

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关于 Hirota 离散 Korteweg-de Vries 方程的三维一致性

Hirota 的离散 Korteweg-de Vries 方程 (dKdV) 是 上的可积偏微分方程，它在连续极限中逼近 Korteweg-de Vries 方程。我们发现了对其他方程的新变换，包括一个二阶二阶偏差分方程，它提供了一个不寻常的嵌入到三维格子中的方法。所得系统的一致性扩展了已广泛用于研究多维格子上的偏差分方程的属性。