On a class of 2D integrable lattice equations
journal contributionposted on 2020-06-25, 12:25 authored by Evgeny FerapontovEvgeny Ferapontov, Ismagil Habibullin, Mariya Kuznetsova, Vladimir NovikovVladimir Novikov
We develop a new approach to the classification of integrable equations of the form uxy = f(u, ux, uy, Δzu Δz¯u, Δ zz¯u) where Δz and Δz¯ 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
Challenges of dispersionless integrability: Hirota type equations
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