Skip to main content
SpringerLink
Log in

New example of a nonlinear hyperbolic equation possessing integrals

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We discover an important new case in the classical problem of the classification of nonlinear hyperbolic equations possessing integrals. In the general (least degenerate) case, in addition, we obtain a formula describing the splitting of the right-hand side of such equations with respect to the first derivatives.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Darboux,Leçons sur la theorie general des surface, Vol. 2, Hermann, Paris (1915).

    Google Scholar 

  2. E. Goursat,Leçons sur l'intégration des équations aux dérivées partielles du second ordre à deux variables indépendantes, Vols. 1, 2, Hermann, Paris (1896, 1898).

    Google Scholar 

  3. E. Vessiot,J. Math. Pure Appl.,18, 1–61 (1939).

    MATH  MathSciNet  Google Scholar 

  4. A. V. Zhiber,Russ. Acad. Sci. Izv. Math.,45, No. 1, 33–54 (1995).

    Article  MathSciNet  Google Scholar 

  5. A. V. Zhiber, “Higher symmetries of the Liouville-type equations”, in:Proc. All-Russ. Conf. “Physics of Condensed Matter” (K. B. Sabitov, ed.) [in Russian], Vol. 1,Mathematical Methods in Physics, Sterlitamak Branch, Acad. Sci. Rep. of Bashkiria, SSPI (1997), pp. 54–57.

  6. M. Yu. Zvyagin,Sov. Math. Dokl.,43, 30–34 (1991).

    MATH  MathSciNet  Google Scholar 

  7. A. B. Borisov and S. A. Zykov,Theor. Math. Phys.,115, 530–541 (1998).

    MATH  MathSciNet  Google Scholar 

  8. A. V. Zhiber and A. B. Shabat,Sov. Math. Dokl.,30, 23–26 (1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mechanics, Ufa Science Center, RAS, Ufa, Russia

    A. V. Zhiber

  2. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

    V. V. Sokolov

Authors
  1. A. V. Zhiber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 1, pp. 20–26, July, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhiber, A.V., Sokolov, V.V. New example of a nonlinear hyperbolic equation possessing integrals. Theor Math Phys 120, 834–839 (1999). https://doi.org/10.1007/BF02557393

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02557393

Keywords

Search

Navigation