An extension of the Kadomtsev-Petviashvili hierarchy and its Hamiltonian structures

TL;DR

This paper extends the KP hierarchy to a two-component version using pseudo-differential operators and constructs its Hamiltonian structures via the R-matrix formalism, advancing the mathematical understanding of integrable systems.

Contribution

It introduces a novel two-component extension of the KP hierarchy and develops its Hamiltonian structures using the R-matrix approach, which was not previously established.

Findings

Constructed a two-component KP hierarchy using pseudo-differential operators

Developed Hamiltonian structures for the extended hierarchy

Applied R-matrix formalism to derive integrability properties

Abstract

In this note we consider a two-component extension of the Kadomtsev-Petviashvili (KP) hierarchy represented with two types of pseudo-differential operators, and construct its Hamiltonian structures by using the $R$-matrix formalism.