Cauchy matrix approach to novel extended semi-discrete KP-type systems

TL;DR

This paper develops a Cauchy matrix approach to construct novel extended semi-discrete KP-type systems, incorporating arbitrary functions to generate diverse solutions beyond traditional solitons.

Contribution

It introduces new extended semi-discrete KP systems and demonstrates how to generate a variety of solutions using the Cauchy matrix approach with arbitrary functions.

Findings

Introduction of bilinear Dδ2KP, extended Dδ2pKP, Dδ2pmKP, and Dδ2SKP systems.

Implementation of arbitrary functions to extend integrable systems.

Generation of diverse solutions beyond standard soliton solutions.

Abstract

Two novel extended semi-discrete KP-type systems, namely partial differential-difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the plane wave factor allows the implementation of extended integrable systems within the Cauchy matrix approach. We introduce the bilinear D\delta2KP system, the extended D\delta2pKP, D\delta2pmKP, and D\delta2SKP systems, all of which are based on the Cauchy matrix approach. This results in a diversity of solutions for these extended systems as contrasted to the usual multiple soliton solutions.