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}
}
  • I. HabibullinM. Poptsova
  • Published 29 March 2017
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
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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