Skip to main content
SpringerLink
Log in

Hyperbolic Equations Admitting Differential Substitutions

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

Abstract

We show that the first n−1 Laplace invariants of a scalar hyperbolic equation obtained from an equation of the same form under a differential substitution of the nth order have a zeroth order with respect to one of the characteristics. It follows that all Laplace invariants of an equation admitting substitutions of an arbitrarily high order must have a zeroth order. Three special cases of such equations are considered: those admitting autosubstitutions, those obtained from a linear equation by a differential substitution, and those with solutions depending simultaneously on both an arbitrary function of x and an arbitrary function of y.

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. A. V. Zhiber, V. V. Sokolov, and S. Ya. Startsev, Dokl. Math., 52, No. 6, 128 (1995).

    Google Scholar 

  2. V. V. Sokolov and A. V. Zhiber, Phys. Lett. A, 208, 303 (1995).

    Google Scholar 

  3. I. M. Anderson and N. Kamran, Duke Math. J., 87, No. 2, 265 (1997).

    Google Scholar 

  4. I. M. Anderson and M. Juras, Duke Math. J., 89, No. 2, 351 (1997).

    Google Scholar 

  5. S. Ya. Startsev, Theor. Math. Phys., 116, 1001 (1998).

    Google Scholar 

  6. S. Ya. Startsev, Theor. Math. Phys., 120, 1009 (1999).

    Google Scholar 

  7. V. E. Adler and S. Ya. Startsev, Theor. Math. Phys., 121, 1484 (1999).

    Google Scholar 

  8. M. Yu. Zvyagin, Sov. Math. Dokl., 43, No. 1, 30 (1991).

    Google Scholar 

  9. V. S. Novikov, Theor. Math. Phys., 116, 890 (1998).

    Google Scholar 

  10. V. V. Sokolov and S. I. Svinolupov, Eur. J. Appl. Math., 6, 145 (1995).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computation Center, Ufa Science Center, RAS, Ufa, Russia

    S. Ya. Startsev

Authors
  1. S. Ya. Startsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Startsev, S.Y. Hyperbolic Equations Admitting Differential Substitutions. Theoretical and Mathematical Physics 127, 460–470 (2001). https://doi.org/10.1023/A:1010359808044

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010359808044

Keywords

Search

Navigation