### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 097, 16 pages      arXiv:1110.5021      https://doi.org/10.3842/SIGMA.2011.097
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

### Symmetries of the Continuous and Discrete Krichever-Novikov Equation

Decio Levi a, Pavel Winternitz b and Ravil I. Yamilov c
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

Received June 16, 2011, in final form October 15, 2011; Published online October 23, 2011

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≤n≤5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases.

Key words: symmetry classification; integrable PDEs; integrable differential-difference equations.

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