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
Funding
Challenges of dispersionless integrability: Hirota type equations
Engineering and Physical Sciences Research Council
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Journal of Mathematical Physics, 61 (7), 073505 and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0013697.