Skip to main content
SpringerLink
Log in

Constructing symmetries and finding a first integral of a system of partial differential-difference equations

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We obtain necessary and sufficient conditions for a system of partial differential-difference equations to admit a group of infinitesimal point transformations. We use examples to illustrate how one can find such groups and generators of symmetries as well as first integrals and functionals for potential operators.

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. Olver, P., Applications of Lie Groups to Differential Equations, New York: Springer-Verlag, 1986. Translated under the title Prilozhenie grupp Li k differentsial’nym uravneniyam, Moscow: Mir, 1989.

    MATH  Google Scholar 

  2. Skubachevskii, A.L. and Shamin, R.V., Second-Order Parabolic Differential-Difference Equations, Dokl. Akad. Nauk, 2001, vol. 39, no. 5, pp. 735–738.

    MathSciNet  Google Scholar 

  3. Kolesnikova, I.A. and Savchin, V.M., On the Existence of Variational Principles for a Class of the Evolutionary Differential-Difference Equations, J. Funct. Spaces Appl., 2012, Article ID 780382.

    Google Scholar 

  4. Skubachevskii, A.L., Elliptic Functional Differential Equations and Applications, Basel-Boston-Berlin, 1997.

    MATH  Google Scholar 

  5. Filippov, V.M., Savchin, V.M., and Shorokhov, S.G., Variational Principles for Nonpotential Operators, Sovr. Probl. Mat. Nov. Dostizh., 1992, vol. 40.

  6. El’sgol’ts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial’nykh uravnenii s otklonyayushchimsya argumentom (Introduction to the Theory of Differential Equations with Deviating Argument), Moscow: Nauka, 1971.

    Google Scholar 

  7. Kolesnikova, I.A., Necessary and Sufficient Conditions for the Existence of Symmetry Groups for Systems of Differential-Difference Equations with Partial Derivatives, J. Math. Sci., 2012, vol. 180, no. 6, pp. 673–684.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    I. A. Kolesnikova

Authors
  1. I. A. Kolesnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Kolesnikova.

Additional information

Original Russian Text © I.A. Kolesnikova, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 193–200.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolesnikova, I.A. Constructing symmetries and finding a first integral of a system of partial differential-difference equations. Diff Equat 51, 196–203 (2015). https://doi.org/10.1134/S0012266115020056

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266115020056

Keywords

Search

Navigation