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
Datum:2019
Hauptverfasser: Garifullin, R.N., Yamilov, R.I.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2019
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
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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.
first_indexed 2025-12-07T21:24:50Z
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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
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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).
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
Article
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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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