### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 120, 7 pages      arXiv:1809.00271      https://doi.org/10.3842/SIGMA.2018.120

### Simple Lax Description of the ILW Hierarchy

Alexandr Buryak ab and Paolo Rossi c
a) School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
b) Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, GSP-1, 119991, Russia
c) Dipartimento di Matematica ''Tullio Levi-Civita'', Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy

Received September 07, 2018, in final form November 06, 2018; Published online November 10, 2018; Author's affiliations corrected November 28, 2018

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.

Key words: intermediate long wave hierarchy; ILW; Lax representation; integrable systems; Hamiltonian.

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