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Fundam. Prikl. Mat., 2006, Volume 12, Issue 7, Pages 65–78 (Mi fpm1017)  

This article is cited in 11 scientific papers (total in 11 papers)

On the characteristic Lie algebras for equations $u_{xy}=f(u,u_x)$

A. V. Zhibera, R. D. Murtazinab

a Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
b Ufa State Aviation Technical University

Abstract: A new approach to classification of integrable nonlinear equations is proposed. The method is based on description of the structure of the characteristic algebra. A basis of the characteristic algebra is constructed for the $\mathrm{sinh}$-Gordon equation.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:4, 3112–3122

Bibliographic databases:

UDC: 517.957

Citation: A. V. Zhiber, R. D. Murtazina, “On the characteristic Lie algebras for equations $u_{xy}=f(u,u_x)$”, Fundam. Prikl. Mat., 12:7 (2006), 65–78; J. Math. Sci., 151:4 (2008), 3112–3122

Citation in format AMSBIB
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\by A.~V.~Zhiber, R.~D.~Murtazina
\paper On the characteristic Lie algebras for equations $u_{xy}=f(u,u_x)$
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 7
\pages 65--78
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\zmath{https://zbmath.org/?q=an:1158.35312}
\elib{http://elibrary.ru/item.asp?id=11143821}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 4
\pages 3112--3122
\crossref{https://doi.org/10.1007/s10958-008-9028-0}
\elib{http://elibrary.ru/item.asp?id=13577639}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49349113410}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Habibullin I., Zheltukhina N., Pekcan A., “On the classification of Darboux integrable chains”, J. Math. Phys., 49:10 (2008), 102702, 39 pp.  crossref  mathscinet  zmath  adsnasa  isi
    2. N. A. Zheltukhina, A. U. Sakieva, I. T. Khabibullin, “Kharakteristicheskaya algebra Li i integriruemye po Darbu diskretnye tsepochki”, Ufimsk. matem. zhurn., 2:4 (2010), 39–51  mathnet  zmath  elib
    3. Habibullin I., Zheltukhina N., Sakieva A., “On Darboux-integrable semi-discrete chains”, J. Phys. A, 43:43 (2010), 434017, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Habibullin I.T., Gudkova E.V., “Classification of integrable discrete Klein–Gordon models”, Phys. Scripta, 83:4 (2011), 045003  crossref  zmath  adsnasa  isi  elib
    5. Kostrigina O.S., Zhiber A.V., “Darboux-integrable two-component nonlinear hyperbolic systems of equations”, J. Math. Phys., 52:3 (2011), 033503, 32 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. I. T. Habibullin, E. V. Gudkova, “An algebraic method for classifying S-integrable discrete models”, Theoret. and Math. Phys., 167:3 (2011), 751–761  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    7. Garifullin R.N., Gudkova E.V., Habibullin I.T., “Method for searching higher symmetries for quad-graph equations”, J. Phys. A: Math. Theor., 44:32 (2011), 325202  crossref  mathscinet  zmath  isi
    8. M. Gyurses, A. V. Zhiber, I. T. Khabibullin, “Kharakteristicheskie koltsa Li differentsialnykh uravnenii”, Ufimsk. matem. zhurn., 4:1 (2012), 53–62  mathnet
    9. A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, “Kharakteristicheskie koltsa Li i integriruemye modeli matematicheskoi fiziki”, Ufimsk. matem. zhurn., 4:3 (2012), 17–85  mathnet  mathscinet
    10. D. V. Millionshchikov, “Characteristic Lie algebras of the sinh-Gordon and Tzitzeica equations”, Russian Math. Surveys, 72:6 (2017), 1174–1176  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  isi
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