Email this article Integrable Two-Dimensional Lattices. Characteristic Lie Rings and Classification
- Authors: Habibullin I.T.1,2, Poptsova M.N.1
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Affiliations:
- Institute of Mathematics, Ufa Scientific Center of the Russian Academy of Sciences
- Bashkir State University
- Issue: Vol 241, No 4 (2019)
- Pages: 396-408
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242902
- DOI: https://doi.org/10.1007/s10958-019-04432-5
- ID: 242902
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Abstract
This paper is devoted to the problem of classification of integrable nonlinear models with three independent variables. The classification algorithm based on the notion of characteristic Lie rings is applied to a class of two-dimensional lattices of hydrodynamic type. By imposing appropriate cutting-off boundary conditions, we reduce the lattice to a system of hyperbolic equations, which is assumed to be a Darboux integrable system. As a result, we found a new integrable lattice.
About the authors
I. T. Habibullin
Institute of Mathematics, Ufa Scientific Center of the Russian Academy of Sciences; Bashkir State University
Author for correspondence.
Email: habibullinismagil@gmail.com
Russian Federation, Ufa; Ufa
M. N. Poptsova
Institute of Mathematics, Ufa Scientific Center of the Russian Academy of Sciences
Email: habibullinismagil@gmail.com
Russian Federation, Ufa
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