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 30–42 (Mi into232)  
This article is cited in 3 scientific papers (total in 3 papers)

On one integrable discrete system

E. V. Pavlovaa, I. T. Habibullinbc, A. R. Khakimovac

a Ufa State Petroleum Technological University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
c Bashkir State University, Ufa
Full-text PDF (183 kB) Citations (3)
Abstract: In this paper, we study a system of nonlinear equations on a square graph related to the affine algebra $A^{(1)}_1$. This system is the simplest representative of the class of discrete systems corresponding to affine Lie algebras. We find the Lax representation and construct hierarchies of higher symmetries. In neighborhoods of singular points $\lambda=0$ and $\lambda=\infty$, we construct formal asymptotic expansions of eigenfunctions of the Lax pair and, based on these expansions, find series of local conservation laws for the system considered.
Keywords: Lax pair, higher symmetry, conservation law, recursion operator, formal diagonalization.
Funding agency Grant number
Russian Science Foundation 15-11-20007
The work of I. T. Habibullin and A. R. Khakimova was supported by the Russian Scientific Foundation (project No. 15-11-20007).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 4, Pages 409–422
DOI: https://doi.org/10.1007/s10958-019-04433-4
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35Q51, 37K60
Language: Russian
Citation: E. V. Pavlova, I. T. Habibullin, A. R. Khakimova, “On one integrable discrete system”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 140, VINITI, M., 2017, 30–42; Journal of Mathematical Sciences, 241:4 (2019), 409–422
Citation in format AMSBIB
\Bibitem{PavHabKha17}
\by E.~V.~Pavlova, I.~T.~Habibullin, A.~R.~Khakimova
\paper On one integrable discrete system
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 140
\pages 30--42
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into232}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799893}
\zmath{https://zbmath.org/?q=an:1423.35329}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 4
\pages 409--422
\crossref{https://doi.org/10.1007/s10958-019-04433-4}
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    • This publication is cited in the following 3 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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