发表机构
Newtouch Center for Mathematics of Shanghai University; SISSA, International School for Advanced Studies; INFN, Sezione di Trieste; Department of Mathematical and Physical Sciences, La Trobe University; Department of Mathematics, Shanghai University（上海大学新触数学中心; 国际高等研究院; 意大利国家核物理研究所的里雅斯特分部; 拉筹伯大学数理科学学院; 上海大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过齐次与非齐次非局部$\bar{\boldsymbol{\nabla}}$问题定义格点KP类方程Lax对的本征函数，推导多种格点KP型方程的新表述并给出显式解，展现同一方程不同表述的差异。
AI 中文摘要
本文构建了格点Kadomtsev-Petviashvili（KP）型本征函数方程。研究考虑齐次非局部$\bar{\boldsymbol{\nabla}}$问题，借此定义格点KP方程Lax对的本征函数。该本征函数结合其在无穷远和有限解析点处的展开，给出了格点修正KP方程、格点Schwarzian KP方程以及Nijhoff-Quispel-Capel KP（NQC-KP）方程的表述形式。本文还考虑了非齐次非局部$\bar{\boldsymbol{\nabla}}$问题，它定义了格点修正KP方程Lax对的本征函数，该本征函数生成了NQC-KP方程的一种不同于已有结果的直接表述。文中得到了这些方程的显式解，可借此看出同一方程不同表述之间的差异。
英文摘要
In this paper, we construct the lattice Kadomtsev-Petviashvili (KP) type eigenfunction equations. A homogeneous nonlocal $\bar{\partial}$ problem is considered, from which we are able to define the eigenfunction of the Lax pair of the lattice KP equation. The eigenfunction together with its expansions at infinity and at a finite analytic point provide formulations of the lattice modified KP equation, the lattice Schwarzian KP equation and the Nijhoff-Quispel-Capel KP (NQC-KP) equation. We also consider an inhomogeneous nonlocal $\bar{\partial}$ problem. It defines the eigenfunction of the Lax pair of the lattice modified KP equation. This eigenfunction generates a direct formulation for the NQC-KP equation, which is different from the previous ones. Explicit solutions of these equations are obtained, from which we can see the difference of the different formulations for same equations.
