Integrable Möbius invariant evolutionary lattices of second order

Abstract

We solve the classification problem for integrable lattices of the form $u_{,t}=f(u_{-2},\dots ,u_2)$ under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains 5 equations, including 3 new. Difference Miura type substitutions are found which relate these equations with known polynomial lattices. We also present some classification results for the generic lattices.

14 pages

References in corpus (1)

• The lattice Schwarzian KdV equation and its symmetries

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