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 137, Pages 17–25 (Mi into203)  
This article is cited in 2 scientific papers (total in 2 papers)

Special class of of Liouville-type hyperbolic equations

A. V. Zhibera, A. M. Yur'evab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Bashkir State University, Ufa
Full-text PDF (167 kB) Citations (2)
Abstract: In this paper, we obtain differential substitutions for a special class of Liouville-type equations that simplify these equations. We present necessary and sufficient conditions of the existence of $y$-integrals of the second order. We examine the principal case of necessary and sufficient conditions of the existence of $y$-integrals.
Keywords: $x$-integral, $y$-integral, Liouville-type equation, differential substitution.
Funding agency Grant number
Russian Science Foundation 15-11-20007
This work was supported by the Russian Scientific Foundation (project No. 15-11-20007).
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 236, Issue 6, Pages 594–602
DOI: https://doi.org/10.1007/s10958-018-4135-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35Q51, 37K60
Language: Russian
Citation: A. V. Zhiber, A. M. Yur'eva, “Special class of of Liouville-type hyperbolic equations”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 137, VINITI, Moscow, 2017, 17–25; J. Math. Sci. (N. Y.), 236:6 (2019), 594–602
Citation in format AMSBIB
\Bibitem{ZhiYur17}
\by A.~V.~Zhiber, A.~M.~Yur'eva
\paper Special class of of Liouville-type hyperbolic equations
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 137
\pages 17--25
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801258}
\zmath{https://zbmath.org/?q=an:1416.35228}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 236
\issue 6
\pages 594--602
\crossref{https://doi.org/10.1007/s10958-018-4135-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059325560}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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