A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

TL;DR

This paper explores the semi-discrete Kadomtsev-Petviashvili (KP) equation, establishing its solutions and deriving a coupled integrable system, thus advancing understanding of semi-discrete integrable systems.

Contribution

It introduces the semi-discrete bilinear KP equation, provides its determinant solutions, and derives a coupled integrable system using Pfaffianization, filling a gap in existing literature.

Findings

Presented Casorati and Grammian determinant solutions for the semi-discrete KP equation

Derived a coupled integrable system via Pfaffianization

Connected continuum limits of Hirota-Miwa equations to semi-discrete systems

Abstract

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.