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Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings
Ismagil Habibullin, Mariya Poptsova Ufa Institute of Mathematics, 112 Chernyshevsky Str., Ufa 450008, Russia
Аннотация:
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 detect the Darboux integrability of the hyperbolic type system we use an algebraic criterion of Darboux integrability which claims that the characteristic Lie rings of such a system must be of finite dimension. We prove that up to the point transformations only one lattice in the studied class passes the test. The lattice coincides with the earlier found Ferapontov–Shabat–Yamilov equation. The one-dimensional reduction $x=y$ of this lattice passes also the symmetry integrability test.
Ключевые слова:
two-dimensional integrable lattice; cut-off boundary condition; open chain; Darboux integrable system; characteristic Lie ring.
Поступила: 30 марта 2017 г.; в окончательном варианте 24 августа 2017 г.; опубликована 7 сентября 2017 г.
Образец цитирования:
Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 073, 26 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1273 https://www.mathnet.ru/rus/sigma/v13/p73
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