# Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings

@article{Habibullin2017ClassificationOA, title={Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings}, author={Ismagil Talgatovich Habibullin and M. N. Poptsova}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2017}, volume={13}, pages={073} }

The main goal of the article is testing a new classification algorithm. To this end we apply it to a relevant problem of describing the integrable cases of a subclass of two-dimensional lattices. By imposing the cut-off conditions $u_{-1}=c_0$ and $u_{N+1}=c_1$ we reduce the lattice $u_{n,xy}=\alpha(u_{n+1},u_n,u_{n-1})u_{n,x}u_{n,y}$ to a finite system of hyperbolic type PDE. Assuming that for each natural $N$ the obtained system is integrable in the sense of Darboux we look for $\alpha$. To…

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