Simple Lax Description of the ILW Hierarchy

TL;DR

This paper provides a straightforward Lax operator formulation for the entire ILW hierarchy, including explicit higher flows and Hamiltonian structures, enhancing understanding of its integrability.

Contribution

It introduces a simple Lax description for the ILW hierarchy, explicitly detailing higher flows and Hamiltonian structures using a single Lax difference-differential operator.

Findings

Explicit Lax difference-differential operator for ILW hierarchy

Complete description of higher flows and Hamiltonian structures

Simplifies the integrability framework of ILW equations

Abstract

In this note we present a simple Lax description of the hierarchy of the intermediate long wave equation (ILW hierarchy). Although the linear inverse scattering problem for the ILW equation itself was well known, here we give an explicit expression for all higher flows and their Hamiltonian structure in terms of a single Lax difference-differential operator.