Lax Pair for a Novel Two-Dimensional Lattice

In the paper by I.T. Habibullin and our joint paper, the algorithm for the classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the chara...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2021
Main Author: Kuznetsova, Maria N.
Format: Article
Language:English
Published: Інститут математики НАН України 2021
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211439
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Lax Pair for a Novel Two-Dimensional Lattice. Maria N. Kuznetsova. SIGMA 17 (2021), 088, 13 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Kuznetsova, Maria N.
author_facet Kuznetsova, Maria N.
citation_txt Lax Pair for a Novel Two-Dimensional Lattice. Maria N. Kuznetsova. SIGMA 17 (2021), 088, 13 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In the paper by I.T. Habibullin and our joint paper, the algorithm for the classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the characteristic Lie-Rinehart algebras. The method was applied for the classification of integrable cases of different subclasses of equations ₙ‚ₓy = (ₙ₊₁, ₙ, ₙ₋₁, ₙ‚ₓ, ₙ,y) of special forms. Under this approach, the novel integrable chain was obtained. In the present paper, we construct a Lax pair for the novel chain. To construct the Lax pair, we use the scheme suggested in papers by E.V. Ferapontov. We also study the periodic reduction of the chain.
first_indexed 2026-03-13T03:06:00Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-13T03:06:00Z
publishDate 2021
publisher Інститут математики НАН України
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spelling Kuznetsova, Maria N.
2026-01-02T08:33:46Z
2021
Lax Pair for a Novel Two-Dimensional Lattice. Maria N. Kuznetsova. SIGMA 17 (2021), 088, 13 pages
1815-0659
2020 Mathematics Subject Classification: 37K10; 37K30; 37D99
arXiv:2102.04207
https://nasplib.isofts.kiev.ua/handle/123456789/211439
https://doi.org/10.3842/SIGMA.2021.088
In the paper by I.T. Habibullin and our joint paper, the algorithm for the classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the characteristic Lie-Rinehart algebras. The method was applied for the classification of integrable cases of different subclasses of equations ₙ‚ₓy = (ₙ₊₁, ₙ, ₙ₋₁, ₙ‚ₓ, ₙ,y) of special forms. Under this approach, the novel integrable chain was obtained. In the present paper, we construct a Lax pair for the novel chain. To construct the Lax pair, we use the scheme suggested in papers by E.V. Ferapontov. We also study the periodic reduction of the chain.
The author gratefully thanks I.T. Habibulin for assigning the problem and useful discussions, E.V. Ferapontov for explaining the method of the construction of Lax pairs, and S.Ya. Startsev for valuable comments. The author gratefully thanks anonymous referees for their contribution to improving the paper.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Lax Pair for a Novel Two-Dimensional Lattice
Article
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spellingShingle Lax Pair for a Novel Two-Dimensional Lattice
Kuznetsova, Maria N.
title Lax Pair for a Novel Two-Dimensional Lattice
title_full Lax Pair for a Novel Two-Dimensional Lattice
title_fullStr Lax Pair for a Novel Two-Dimensional Lattice
title_full_unstemmed Lax Pair for a Novel Two-Dimensional Lattice
title_short Lax Pair for a Novel Two-Dimensional Lattice
title_sort lax pair for a novel two-dimensional lattice
url https://nasplib.isofts.kiev.ua/handle/123456789/211439
work_keys_str_mv AT kuznetsovamarian laxpairforanoveltwodimensionallattice