Integrable Möbius-invariant evolutionary lattices of second order

Resumo

We solve the classification problem for integrable lattices of the form u,_t = f(u₋₂,..., u₂) under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains five equations, including three new ones. Difference Miura-type substitutions are found, which relate these equations to known polynomial lattices. We also present some classification results for generic lattices.