On the Fourth-Order Lattice Gel'fand-Dikii Equations
The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be vie...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211877 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Fourth-Order Lattice Gel'fand-Dikii Equations. Guesh Yfter Tela, Song-Lin Zhao and Da-Jun Zhang. SIGMA 19 (2023), 007, 30 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736892340994048 |
|---|---|
| author | Tela, Guesh Yfter Zhao, Song-Lin Zhang, Da-Jun |
| author_facet | Tela, Guesh Yfter Zhao, Song-Lin Zhang, Da-Jun |
| citation_txt | On the Fourth-Order Lattice Gel'fand-Dikii Equations. Guesh Yfter Tela, Song-Lin Zhao and Da-Jun Zhang. SIGMA 19 (2023), 007, 30 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be viewed as higher-order members of the extended lattice Boussinesq-type equations. The resulting lattice equations given here are in five-component form, and some of them are multidimensionally consistent by introducing extra equations. Lax integrability is discussed both by a direct linearization scheme and also through a multi-dimensional consistent property. Some reductions of the five-component lattice equations to the four-component forms are considered.
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| first_indexed | 2026-04-17T16:45:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211877 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:45:32Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tela, Guesh Yfter Zhao, Song-Lin Zhang, Da-Jun 2026-01-14T09:55:44Z 2023 On the Fourth-Order Lattice Gel'fand-Dikii Equations. Guesh Yfter Tela, Song-Lin Zhao and Da-Jun Zhang. SIGMA 19 (2023), 007, 30 pages 1815-0659 2020 Mathematics Subject Classification: 35Q51; 35Q55 arXiv:2206.14403 https://nasplib.isofts.kiev.ua/handle/123456789/211877 https://doi.org/10.3842/SIGMA.2023.007 The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be viewed as higher-order members of the extended lattice Boussinesq-type equations. The resulting lattice equations given here are in five-component form, and some of them are multidimensionally consistent by introducing extra equations. Lax integrability is discussed both by a direct linearization scheme and also through a multi-dimensional consistent property. Some reductions of the five-component lattice equations to the four-component forms are considered. The authors are grateful to the referees for their invaluable comments. This work is supported by the National Natural Science Foundation of China (grant nos. 12271334, 12071432, 11875040). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Fourth-Order Lattice Gel'fand-Dikii Equations Article published earlier |
| spellingShingle | On the Fourth-Order Lattice Gel'fand-Dikii Equations Tela, Guesh Yfter Zhao, Song-Lin Zhang, Da-Jun |
| title | On the Fourth-Order Lattice Gel'fand-Dikii Equations |
| title_full | On the Fourth-Order Lattice Gel'fand-Dikii Equations |
| title_fullStr | On the Fourth-Order Lattice Gel'fand-Dikii Equations |
| title_full_unstemmed | On the Fourth-Order Lattice Gel'fand-Dikii Equations |
| title_short | On the Fourth-Order Lattice Gel'fand-Dikii Equations |
| title_sort | on the fourth-order lattice gel'fand-dikii equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211877 |
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