Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 140, Pages 18–29 (Mi into231)  
This article is cited in 1 scientific paper (total in 1 paper)

Integrable two-dimensional lattices. Characteristic Lie rings and classification

I. T. Habibullinab, M. N. Poptsovaa

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Bashkir State University, Ufa
Full-text PDF (186 kB) Citations (1)
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 the two-dimensional lattices of hydrodynamic type. By imposing appropriate cutting-off boundary conditions, we reduce the lattice to a system of the hyperbolic equations, which is assumed to be a Darboux integrable system. As a result, we found a new integrable lattice.
Keywords: integrable two-dimensional lattice, characteristic Lie ring, Darboux integrable system.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-97008-Поволжье-a
This work is supported by the Russian Foundation for Basic Research (project Volga Region No. 14-01-97008-a).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 4, Pages 396–408
DOI: https://doi.org/10.1007/s10958-019-04432-5
Bibliographic databases:
Document Type: Article
UDC: 517.962.9
MSC: 35L10, 39A14
Language: Russian
Citation: I. T. Habibullin, M. N. Poptsova, “Integrable two-dimensional lattices. Characteristic Lie rings and classification”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 140, VINITI, M., 2017, 18–29; Journal of Mathematical Sciences, 241:4 (2019), 396–408
Citation in format AMSBIB
\Bibitem{HabKuz17}
\by I.~T.~Habibullin, M.~N.~Poptsova
\paper Integrable two-dimensional lattices. Characteristic Lie rings and classification
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 140
\pages 18--29
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into231}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799892}
\zmath{https://zbmath.org/?q=an:1427.39009}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 4
\pages 396--408
\crossref{https://doi.org/10.1007/s10958-019-04432-5}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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