Symmetries of the Continuous and Discrete Krichever-Novikov Equation

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

2011-10-23

arxiv.org/abs/1110.5021v1

SIGMA 7 (2011), 097, 16 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2011.097

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.

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