A note on the KP hierarchy

TL;DR

This paper introduces a new bi-Hamiltonian hierarchy related to the KP hierarchy, simplifying its structure and elucidating its Hamiltonian properties through a novel approach based on the two boson representation.

Contribution

It constructs a bi-Hamiltonian hierarchy from the two boson representation, providing a simpler framework that naturally encompasses all Hamiltonian structures of the KP hierarchy.

Findings

New bi-Hamiltonian hierarchy derived from two boson representation

Simplifies understanding of the KP hierarchy's Hamiltonian structures

Shows KP hierarchy as a composite of the new hierarchy

Abstract

Given the two boson representation of the conformal algebra \hat W_\infty, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system.