On nonautonomous differential-difference AKP, BKP and CKP equations

TL;DR

This paper introduces six new nonautonomous differential-difference equations related to the discrete Kadomtsev-Petviashvili hierarchy, demonstrating their integrability and soliton solutions through the direct linearisation framework.

Contribution

The paper extends the direct linearisation method to establish six novel nonautonomous differential-difference equations within the KP hierarchy classes.

Findings

Six new integrable nonautonomous equations are constructed.

All models possess soliton solutions and multi-dimensional consistency.

Equations include (2+2)-dimensional forms in BKP and CKP classes.

Abstract

Based on the direct linearisation framework of the discrete Kadomtsev-Petviashvili-type equations presented in [Proc. R. Soc. A, 473 (2017) 20160915], six novel nonautonomous 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 linearisation.