Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
We consider five-point differential-difference equations. We aim to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications associated with transformations of the first, second, and third orders....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210233 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation / R.N. Garifullin, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862662898869862400 |
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| author | Garifullin, R.N. Yamilov, R.I. |
| author_facet | Garifullin, R.N. Yamilov, R.I. |
| citation_txt | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation / R.N. Garifullin, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider five-point differential-difference equations. We aim to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications associated with transformations of the first, second, and third orders. As far as we know, such a classification problem is solved for the first time in the discrete case. We analyze transformations obtained to specify their nature. A number of new integrable five-point equations and new transformations have been found. Moreover, we have derived a new, completely discrete equation. There are a few non-standard transformations which are of the Miura type or are linearizable in a non-standard way. We have also proved that the orders of possible transformations are restricted by the number five in this problem.
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| first_indexed | 2025-12-07T21:24:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210233 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:50Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Garifullin, R.N. Yamilov, R.I. 2025-12-04T13:05:21Z 2019 Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation / R.N. Garifullin, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 26 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K05; 37K10; 35G20 arXiv: 1903.11893 https://nasplib.isofts.kiev.ua/handle/123456789/210233 https://doi.org/10.3842/SIGMA.2019.062 We consider five-point differential-difference equations. We aim to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications associated with transformations of the first, second, and third orders. As far as we know, such a classification problem is solved for the first time in the discrete case. We analyze transformations obtained to specify their nature. A number of new integrable five-point equations and new transformations have been found. Moreover, we have derived a new, completely discrete equation. There are a few non-standard transformations which are of the Miura type or are linearizable in a non-standard way. We have also proved that the orders of possible transformations are restricted by the number five in this problem. RIY gratefully acknowledges the financial support from the Russian Science Foundation grant (project 15-11-20007). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation Article published earlier |
| spellingShingle | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation Garifullin, R.N. Yamilov, R.I. |
| title | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation |
| title_full | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation |
| title_fullStr | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation |
| title_full_unstemmed | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation |
| title_short | Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation |
| title_sort | integrable modifications of the ito-narita-bogoyavlensky equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210233 |
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