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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 097, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.097 (Mi sigma655) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Symmetries of the Continuous and Discrete Krichever–Novikov Equation

Decio Levia, Pavel Winternitzb, Ravil I. Yamilovc

a Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
b Centre de recherches mathématiques and Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, H3C 3J7, Montréal (Québec), Canada
c Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation
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DOI: https://doi.org/10.3842/SIGMA.2011.097
Abstract: 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 $1\le n\le 5$. The highest dimensions, namely $n=5$ and $n=4$ occur only in the integrable cases.
Keywords: symmetry classification, integrable PDEs, integrable differential-difference equations.
Received: June 16, 2011; in final form October 15, 2011; Published online October 23, 2011
Bibliographic databases:
Document Type: Article
MSC: 35B06; 35K25; 37K10; 39A14
Language: English
Citation: Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.
Citation in format AMSBIB
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\by Decio Levi, Pavel Winternitz, Ravil I. Yamilov
\paper Symmetries of the Continuous and Discrete Krichever--Novikov Equation
\jour SIGMA
\yr 2011
\vol 7
\papernumber 097
\totalpages 16
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