Ferapontov, Evgeny Habibullin, Ismagil Kuznetsova, Mariya Novikov, Vladimir On a class of 2D integrable lattice equations We develop a new approach to the classification of integrable equations of the form u<sub>xy</sub> = f(u, u<sub>x</sub>, u<sub>y</sub>, Δ<sub>z</sub>u Δ<sub>z¯</sub>u, Δ <sub>zz¯</sub>u) where Δ<sub>z </sub> and Δ<sub>z</sub><sub>¯ </sub>are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure which is Einstein-Weyl on every solution. (2) Secondly, to the candidate equations selected at the previous step we apply the test of Darboux integrability of reductions obtained by imposing suitable cut-off conditions Mathematical Physics;Mathematical Sciences;Physical Sciences;Darboux integrability.;dispersionless Lax pair;Einstein-Weyl geometry;characteristic variety;2D lattice equations 2020-06-25
    https://repository.lboro.ac.uk/articles/journal_contribution/On_a_class_of_2D_integrable_lattice_equations/12559481