Skip to main content
SpringerLink
Log in

Bäcklund correspondences for evolution equations in a multidimensional space

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

Abstract

Our objective is to develop a calculation technique that allows performing an effective algebro-geometric (group) analysis of partial differential equations with arbitrarily many independent variables. We completely describe an important class of multidimensional evolution equations admitting Bäcklund correspondences of a given form. In particular, this class is found to be rather wide, although it turns out to be somewhat richer in the one-dimensional case because the requirement that mixed derivatives be equal is absent.

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. V. V. Zharinov, Math. USSR Sb., 64, No. 1, 277–293 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations, World Scientific, Singapore (1992).

    Google Scholar 

  3. I. S. Krasil’shchik and A. M. Vinogradov, Acta Appl. Math., 15, 161–209 (1989).

    MathSciNet  Google Scholar 

  4. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978); English transl., Academic Press, New York (1982); N. Kh. Ibragimov, Transformation Groups Applied to Mathematical Physics [in Russian], Nauka, Moscow (1983); English transl., Reidel, Dordrecht (1987); P. Olver, Applications of Lie Groups to Differential Equations, Springer, New York (1986); A. M. Vinogradov and I. S. Krasil’shchik, eds., Symmetries and Conservation Laws for Equations of Mathematical Physics [in Russian], Factorial, Moscow (1997); English transl.: I. S. Krasil’shchik and A. M. Vinogradov, eds., Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Amer. Math. Soc., Providence, R. I. (1999); B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge Univ. Press, Cambridge (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Steklov Institute of Mathematics, RAS, Moscow, Russia

    V. V. Zharinov

Authors
  1. V. V. Zharinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 3–13, May, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zharinov, V.V. Bäcklund correspondences for evolution equations in a multidimensional space. Theor Math Phys 147, 449–459 (2006). https://doi.org/10.1007/s11232-006-0053-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-006-0053-1

Keywords

Search

Navigation