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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 53–62 (Mi ufa132)  

This article is cited in 2 scientific papers (total in 2 papers)

Characteristic Lie rings of differential equations

M. Gürsesa, A. V. Zhiberb, I. T. Habibullinb

a Bilkent University, Ankara, Turkey
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: The characteristic Lie rings corresponding to hyperbolic type equations are considered. Possible applications of this concept to the problem of integrable classification of systems of the hyperbolic type partial differential equations with more than two characteristic destinations, evolutionary type equations and ordinary differential equations are briefly discussed. The widely known models of mathematical physics as well as the system of “n”-wave equations, the Korteweg-de Vries equation, the Burgers equation and the first Painlevé equation are considered as illustrative examples.

Keywords: characteristic vector fields, characteristic ring, evolution equations, system of “n”-wave equations.

Full text: PDF file (442 kB)
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UDC: 517.9
Received: 25.11.2011

Citation: M. Gürses, A. V. Zhiber, I. T. Habibullin, “Characteristic Lie rings of differential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 53–62

Citation in format AMSBIB
\Bibitem{GurZhiHab12}
\by M.~G\"urses, A.~V.~Zhiber, I.~T.~Habibullin
\paper Characteristic Lie rings of differential equations
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 53--62
\mathnet{http://mi.mathnet.ru/ufa132}


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    This publication is cited in the following articles:
    1. 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
    2. A. U. Sakieva, “Kharakteristicheskoe koltso Li uravneniya Zhibera–Shabata–Tsitseiki”, Ufimsk. matem. zhurn., 4:3 (2012), 155–160  mathnet
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