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
Datum:2011
Hauptverfasser: Levi, D., Winternitz, P., Yamilov, R.I.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2011
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
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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.
first_indexed 2025-11-28T00:02:36Z
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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
record_format dspace
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
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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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AT winternitzp symmetriesofthecontinuousanddiscretekrichevernovikovequation
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