A new extended KP hierarchy

TL;DR

This paper introduces a novel extended KP hierarchy that encompasses new KP equations with sources, offering a unified framework for constructing soliton equations with Lax representations and reductions.

Contribution

It presents a new method to construct an extended KP hierarchy including self-consistent sources and reductions, advancing the theory of integrable systems.

Findings

Includes two types of KP equations with sources

Allows reductions to k-constrained KP and Gelfand-Dickey hierarchies

Provides a general construction method for soliton equations with sources

Abstract

A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It provides a general way to construct soliton equations with sources and their Lax representations.