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TMF, 2011, Volume 166, Number 1, Pages 51–67 (Mi tmf6595)  

This article is cited in 10 scientific papers (total in 10 papers)

Hyperbolic equations with third-order symmetries

A. G. Meshkova, V. V. Sokolovb

a Orel State Technical University, Orel, Russia
b Landau Institute for Theoretical Physics, RAS, Moscow, Russia

Abstract: We present a complete list of nonlinear one-field hyperbolic equations with integrable third-order $x$ and $y$ symmetries. The list includes both equations of the sine-Gordon type and equations linearizable by differential substitutions.

Keywords: higher symmetry, sine-Gordon type equation, Liouville-type equation

DOI: https://doi.org/10.4213/tmf6595

Full text: PDF file (476 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:1, 43–57

Bibliographic databases:

Received: 05.07.2010

Citation: A. G. Meshkov, V. V. Sokolov, “Hyperbolic equations with third-order symmetries”, TMF, 166:1 (2011), 51–67; Theoret. and Math. Phys., 166:1 (2011), 43–57

Citation in format AMSBIB
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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. N. Kuznetsova, “O nelineinykh giperbolicheskikh uravneniyakh, svyazannykh differentsialnymi podstanovkami s uravneniem Kleina–Gordona”, Ufimsk. matem. zhurn., 4:3 (2012), 86–103  mathnet  mathscinet
    2. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    3. Mariya N. Kuznetsova, Asli Pekcan, Anatoliy V. Zhiber, “The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$”, SIGMA, 8 (2012), 090, 37 pp.  mathnet  crossref  mathscinet
    4. Adler V.E. Shabat A.B., “Toward a theory of integrable hyperbolic equations of third order”, J. Phys. A, 45:39 (2012), 395207, 17 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    5. Garifullin R.N. Yamilov R.I., “Generalized symmetry classification of discrete equations of a class depending on twelve parameters”, J. Phys. A, 45:34 (2012), 345205, 23 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    6. Meshkov A. Sokolov V., “Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries”, Lett. Math. Phys., 104:3 (2014), 341–360  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Habibullin I.T. Khakimova A.R. Poptsova M.N., “On a Method For Constructing the Lax pairs For Nonlinear Integrable Equations”, J. Phys. A-Math. Theor., 49:3 (2016), 035202  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
    9. Habibullin I.T. Khakimova A.R., “On a Method For Constructing the Lax pairs For Integrable Models Via a Quadratic Ansatz”, J. Phys. A-Math. Theor., 50:30 (2017), 305206  crossref  mathscinet  zmath  isi  scopus
    10. I. T. Khabibullin, A. R. Khakimova, “Invariantnye mnogoobraziya integriruemykh uravnenii giperbolicheskogo tipa i ikh prilozheniya”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 136–150  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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