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 J. Sib. Fed. Univ. Math. Phys., 2010, Volume 3, Issue 2, Pages 173–184 (Mi jsfu116)

Characteristic algebras of nonlinear hyperbolic systems of equations

Anatoly V. Zhibera, Olga S. Kostriginab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
b Ufa State Aviation Technical University, Ufa, Russia

Abstract: We describe all $n$-component systems of nonlinear hyperbolic equations with a complete set of integrals of the first order and two-component systems of equations with three integrals of the first order and one integral of the second order. Necessary conditions for the existence of two integrals of the first order and two integral of second order for two-component systems of equations are obtained.

Keywords: characteristic algebra, integral, vector field, Riemann tensor.

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UDC: 517.9
Accepted: 10.03.2010

Citation: Anatoly V. Zhiber, Olga S. Kostrigina, “Characteristic algebras of nonlinear hyperbolic systems of equations”, J. Sib. Fed. Univ. Math. Phys., 3:2 (2010), 173–184

Citation in format AMSBIB
\Bibitem{ZhiKos10} \by Anatoly~V.~Zhiber, Olga~S.~Kostrigina \paper Characteristic algebras of nonlinear hyperbolic systems of equations \jour J. Sib. Fed. Univ. Math. Phys. \yr 2010 \vol 3 \issue 2 \pages 173--184 \mathnet{http://mi.mathnet.ru/jsfu116} 

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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. Kostrigina O.S., Zhiber A.V., “Darboux-integrable two-component nonlinear hyperbolic systems of equations”, J. Math. Phys., 52:3 (2011), 033503, 32 pp.
2. M. V. Yangubaeva, “On structure of integrals for systems of discrete equations”, Ufa Math. J., 6:1 (2014), 111–116
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