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 $1\le n\le 5$. The highest dimensions, namely $n=5$ and $n=4$ occur only in the integrable cases.

References in corpus (4)

• Generalized symmetry integrability test for discrete equations on the square lattice
• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
• Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
• Symmetry algebra of discrete KdV equations and corresponding differential-difference equations of Volterra type

Cited by in corpus (9)

• Symmetries and conservation laws of the generalized Krichever-Novikov equation
• Necessary integrability conditions for evolutionary lattice equations
• On the recursion operators for integrable equations
• Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation
• Lie group analysis of a generalized Krichever-Novikov differential-difference equation
• Negative flows and non-autonomous reductions of the Volterra lattice
• A non autonomous generalization of the $Q_{\text{V}}$ equation
• Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation
• Difference Krichever-Novikov operators