Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations. Proc. R. Soc. A 473, 20160915 (doi:10.1098/rspa.2016.0915)), six novel non-autonomous differential-difference equations are established, including three in the AKP class, two in the BKP class and one in the CKP class. In particular, one in the BKP class and the one in the CKP class are both in (2 + 2)-dimensional form. All the six models are integrable in the sense of having the same linear integral equation representations as those of their associated discrete Kadomtsev–Petviashvili-type equations, which guarantees the existence of soliton-type solutions and the multi-dimensional consistency of these new equations from the viewpoint of the direct linearization.

中文翻译：

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关于非自治微分差分 AKP、BKP 和 CKP 方程

基于 Fu & Nijhoff 工作中提出的离散 Kadomtsev-Petviashvili 型方程的直接线性化框架 (Fu W, Nijhoff FW. 2017 Direct linearizing transform for 三维离散可积系统：格子 AKP、BKP 和 CKP 方程. Proc. R. Soc. A 473, 20160915 (doi:10.1098/rspa.2016.0915))，建立了六个新的非自治微分差分方程，其中三个在AKP类中，两个在BKP类中，一个在CKP 类。特别地，BKP类的一个和CKP类的一个都是(2+2)维形式。在具有与其相关的离散 Kadomtsev-Petviashvili 型方程相同的线性积分方程表示的意义上，所有六个模型都是可积分的，