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arXiv · 2005.06738

On a class of 2D integrable lattice equations

E. V. Ferapontov·I. T. Habibullin·M. N. Kuznetsova·V. S. Novikov
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Abstract

We develop a new approach to the classification of integrable equations of the form $$ u_{xy}=f(u, u_x, u_y, \triangle_z u \triangle_{\bar z}u, \triangle_{z\bar z}u), $$ where $\triangle_{ z}$ and $\triangle_{\bar z}$ 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.

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E. V. Ferapontov, I. T. Habibullin, M. N. Kuznetsova, V. S. Novikov. 2020-05-14. On a class of 2D integrable lattice equations. https://doi.org/10.1063/5.0013697

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