Symmetries of the Continuous and Discrete Krichever-Novikov Equation
A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1≤n≤5. The highe...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147657 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Symmetries of the Continuous and Discrete Krichever-Novikov Equation / D. Levi, P. Winternitz, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862600469327642624 |
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| author | Levi, D. Winternitz, P. Yamilov, R.I. |
| author_facet | Levi, D. Winternitz, P. Yamilov, R.I. |
| citation_txt | Symmetries of the Continuous and Discrete Krichever-Novikov Equation / D. Levi, P. Winternitz, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1≤n≤5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases.
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| first_indexed | 2025-11-28T00:02:36Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147657 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T00:02:36Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
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| spelling | Levi, D. Winternitz, P. Yamilov, R.I. 2019-02-15T17:03:19Z 2019-02-15T17:03:19Z 2011 Symmetries of the Continuous and Discrete Krichever-Novikov Equation / D. Levi, P. Winternitz, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35B06; 35K25; 37K10; 39A14 https://nasplib.isofts.kiev.ua/handle/123456789/147657 A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1≤n≤5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases. This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html.
 The research of L.D. has been partly supported by the Italian Ministry of Education and Research, PRIN “Continuous and discrete nonlinear integrable evolutions: from water waves to symplectic maps”. The research of P.W. was partly supported by a research grant from NSERC of Canada. R.I.Y. has been partially supported by the Russian Foundation for Basic Research (grant numbers 10-01-00088-a and 11-01-97005-r-povolzhie-a). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries of the Continuous and Discrete Krichever-Novikov Equation Article published earlier |
| spellingShingle | Symmetries of the Continuous and Discrete Krichever-Novikov Equation Levi, D. Winternitz, P. Yamilov, R.I. |
| title | Symmetries of the Continuous and Discrete Krichever-Novikov Equation |
| title_full | Symmetries of the Continuous and Discrete Krichever-Novikov Equation |
| title_fullStr | Symmetries of the Continuous and Discrete Krichever-Novikov Equation |
| title_full_unstemmed | Symmetries of the Continuous and Discrete Krichever-Novikov Equation |
| title_short | Symmetries of the Continuous and Discrete Krichever-Novikov Equation |
| title_sort | symmetries of the continuous and discrete krichever-novikov equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147657 |
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