Symmetry, Integrability and Geometry: Methods and Applications (Oct 2011)
Symmetries of the Continuous and Discrete Krichever-Novikov Equation
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.