The KdV hierarchy in terms of whole powers of an integro-differential operator

TL;DR

This paper demonstrates that the entire KdV hierarchy and its conservation laws can be represented using the full powers of an integro-differential operator and associated functions, offering a new perspective on integrable systems.

Contribution

It introduces a novel formulation of the KdV hierarchy using whole powers of an integro-differential operator, expanding the mathematical framework of integrable equations.

Findings

Representation of KdV equations via integro-differential operator powers

Expression of conservation laws through these operators

New insights into the structure of integrable hierarchies

Abstract

It is shown that equations of the Korteweg-de Vries hierarchy and their conservation laws can be expressed via the whole powers of an integro-differential operator and functions provided by them.