On a class of 2D integrable lattice equations
Evgeny Ferapontov (1259199), Ismagil Habibullin (9023975), Mariya Kuznetsova (9023978), Vladimir Novikov (1259079)
Abstract
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,\nΔ\n<sub>zz¯</sub>u) where Δ<sub>z </sub> and Δ<sub>z</sub><sub>¯ </sub>are the forward/backward discrete\nderivatives. The following 2-step classification procedure is proposed:\n(1) First we require that the dispersionless limit of the equation is integrable, that is, its\ncharacteristic variety defines a conformal structure which is Einstein-Weyl on every solution.\n(2) Secondly, to the candidate equations selected at the previous step we apply the test of\nDarboux integrability of reductions obtained by imposing suitable cut-off conditions