New solutions to the differential-difference KP equation

In this paper, we study the differential-difference Kadomtsev-Petviashvili (D Delta KP) equation through the dressing method based on a nonlocal (partial derivative) over bar -problem. Cauchy type determinant solution and a new type rational solution are given. The initial value problem of D Delta KP is discussed by virtue of the quasi-local (partial derivative) over bar -problem. From an impulse initial condition, a new explicit solution to the initial value problem of D Delta KP is obtained. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the differential-difference Kadomtsev-Petviashvili equation and its initial value problem, obtaining solutions and new type rational solutions through the dressing method and quasi-local partial derivative-problem.