Geodesic
Integrable M\"obius-invariant evolutionary lattices of second order
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 4, pp. 13-25

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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 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.
Keywords: integrability, symmetry, conservation law, Möbius invariantm cross-ratio. 
@article{FAA_2016_50_4_a2,
     author = {V. E. Adler},
     title = {Integrable {M\"obius-invariant} evolutionary lattices of second order},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {13--25},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_4_a2/}
}
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V. E. Adler. Integrable M\"obius-invariant evolutionary lattices of second order. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 4, pp. 13-25. http://geodesic.mathdoc.fr/item/FAA_2016_50_4_a2/