Generalized Cauchy matrix approach for non-autonomous discrete Kadomtsev-Petviashvili system

TL;DR

This paper develops a generalized Cauchy matrix approach to analyze various non-autonomous discrete KP systems, deriving solutions and discussing Lax representations for these complex integrable equations.

Contribution

It introduces a unified approach for non-autonomous discrete KP equations, including solution derivation and Lax pair analysis, expanding understanding of their integrability.

Findings

Derived multiple solutions including multi-soliton solutions

Unified description of various non-autonomous KP equations

Established Lax representations for these equations

Abstract

In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice potential KP equation, non-autonomous lattice potential modified KP equation, non-autonomous asymmetric lattice potential modified KP equation, non-autonomous lattice Schwarzian KP equation and non-autonomous lattice KP-type Nijhoff-Quispel-Capel equation. By introducing point transformations, all the equations are described as simplified forms, where the lattice parameters are absorbed. Several kinds of solutions more than multi-soliton solutions to these equations are derived by solving determining equation set. Lax representations for these equations are also discussed.