Algebraic identities associated with KP and AKNS hierarchies

TL;DR

This paper introduces algebraic identities involving a quasi-shuffle product that enable the construction of explicit KP and AKNS hierarchy equations, providing a new algebraic approach to integrable systems.

Contribution

It presents a novel algebraic framework using quasi-shuffle products to derive KP and AKNS hierarchies explicitly, advancing the algebraic understanding of integrable systems.

Findings

Derived explicit KP hierarchy equations from algebraic identities.

Established algebraic identities for AKNS hierarchy construction.

Provided a new algebraic method for integrable systems analysis.

Abstract

Explicit KP and AKNS hierarchy equations can be constructed from a certain set of algebraic identities involving a quasi-shuffle product.