Fu Wei, Nijhoff Frank W
School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People's Republic of China.
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
Proc Math Phys Eng Sci. 2021 Jan;477(2245):20200717. doi: 10.1098/rspa.2020.0717. Epub 2021 Jan 20.
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. , 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.
基于傅和尼霍夫（Fu W，Nijhoff FW. 2017三维离散可积系统的直接线性化变换：格点AKP、BKP和CKP方程。《皇家学会学报A》，20160915（doi:10.1098/rspa.2016.0915））工作中提出的离散Kadomtsev-Petviashvili型方程的直接线性化框架，建立了六个新的非自治微分-差分方程，其中包括AKP类中的三个、BKP类中的两个和CKP类中的一个。特别地，BKP类中的一个和CKP类中的一个均为（2 + 2）维形式。从直接线性化的角度来看，所有这六个模型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是可积的，这保证了孤子型解的存在以及这些新方程的多维一致性。
