Simple Lax Description of the ILW Hierarchy

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 structu...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Buryak, A., Rossi, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209837
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Simple Lax Description of the ILW Hierarchy / A. Buryak, P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Buryak, A.
Rossi, P.
author_facet Buryak, A.
Rossi, P.
citation_txt Simple Lax Description of the ILW Hierarchy / A. Buryak, P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 10 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2025-12-07T18:53:20Z
format Article
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id nasplib_isofts_kiev_ua-123456789-209837
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T18:53:20Z
publishDate 2018
publisher Інститут математики НАН України
record_format dspace
spelling Buryak, A.
Rossi, P.
2025-11-27T14:46:18Z
2018
Simple Lax Description of the ILW Hierarchy / A. Buryak, P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 10 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 37K10
arXiv: 1809.00271
https://nasplib.isofts.kiev.ua/handle/123456789/209837
https://doi.org/10.3842/SIGMA.2018.120
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.
We would like to thank Andrea Brini, Guido Carlet, Oleg Chalykh, Allan Fordy, Alexander Mikhailov, and Vladimir Novikov for useful discussions. The work of the first author (Theorem 1, parts 1 and 3) was supported by the grant no. 16-11-10260 of the Russian Science Foundation.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Simple Lax Description of the ILW Hierarchy
Article
published earlier
spellingShingle Simple Lax Description of the ILW Hierarchy
Buryak, A.
Rossi, P.
title Simple Lax Description of the ILW Hierarchy
title_full Simple Lax Description of the ILW Hierarchy
title_fullStr Simple Lax Description of the ILW Hierarchy
title_full_unstemmed Simple Lax Description of the ILW Hierarchy
title_short Simple Lax Description of the ILW Hierarchy
title_sort simple lax description of the ilw hierarchy
url https://nasplib.isofts.kiev.ua/handle/123456789/209837
work_keys_str_mv AT buryaka simplelaxdescriptionoftheilwhierarchy
AT rossip simplelaxdescriptionoftheilwhierarchy