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

💡 Research Summary

The paper undertakes a systematic Lie point symmetry classification of a broad family of differential‑difference equations that depend on nine real parameters. The authors begin by writing the most general scalar lattice equation of the form
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