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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| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| ISSN: | 1815-0659 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211439 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Lax Pair for a Novel Two-Dimensional Lattice. Maria N. Kuznetsova. SIGMA 17 (2021), 088, 13 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862549352653783040 |
|---|---|
| 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.
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| first_indexed | 2026-03-13T03:06:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211439 |
| 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 |
| record_format | dspace |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lax Pair for a Novel Two-Dimensional Lattice Article published earlier |
| 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 |