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TMF, 2009, Volume 161, Number 2, Pages 176–190 (Mi tmf6430)  

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

Vector hyperbolic equations with higher symmetries

A. G. Meshkov

Orel State University for Technology, Orel, Russia

Abstract: We list eleven vector hyperbolic equations that have third-order symmetries with respect to both characteristics. This list exhausts the equations with at least one symmetry of a divergence form. We integrate four equations in the list explicitly, bring one to a linear form, and bring four more to nonlinear ordinary nonautonomous systems. We find the Bäcklund transformations for six equations.

Keywords: hyperbolic equation, higher symmetry, integral, Bäcklund transformation, exact integrability

DOI: https://doi.org/10.4213/tmf6430

Full text: PDF file (471 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 161:2, 1471–1484

Bibliographic databases:

Received: 30.04.2008
Revised: 15.04.2009

Citation: A. G. Meshkov, “Vector hyperbolic equations with higher symmetries”, TMF, 161:2 (2009), 176–190; Theoret. and Math. Phys., 161:2 (2009), 1471–1484

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6430
  • http://mi.mathnet.ru/eng/tmf/v161/i2/p176

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$”, Math. Notes, 89:2 (2011), 184–193  mathnet  crossref  crossref  mathscinet  isi
    2. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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