Integrable Möbius-invariant evolutionary lattices of second order
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We solve the classification problem for integrable lattices of the form u, t = f(u −2,..., u 2) 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.
Key wordsintegrability symmetry conservation law Möbius invariant cross-ratio
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