Skip to main content
SpringerLink
Log in

Relationship between Symmetries andConservation Laws

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The fundamental relation between Lie-Bäcklund symmetry generators andconservation laws of an arbitrary differential equation is derived without regardto a Lagrangian formulation of the differential equation. This relation is used inthe construction of conservation laws for partial differential equations irrespectiveof the knowledge or existence of a Lagrangian. The relation enables one toassociate symmetries to a given conservation law of a differential equation.Applications of these results are illustrated for a range of examples.

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

REFERENCES

  • Anco, S. C., and Bluman, G. (1996). J. Math. Phys. 37, 2361.

    Google Scholar 

  • Anderson, I. M., and Duchamp, T. E. (1980). Am. J. Math. 102, 781.

    Google Scholar 

  • Anderson, I. M., and Duchamp, T. E. (1984). J. Differential Equations 51, 1.

    Google Scholar 

  • Anderson, R. L., and Ibragimov, N. H. (1994). In CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, Ibragimov, N. H., ed., CRC Press, Boca Raton, Florida, Chapter 6, p. 62.

    Google Scholar 

  • Anderson, R. L., and Ibragimov, N. H. (1995). In Modern Group Theoretical Methods in Physics, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Anderson, R. L., and Ibragimov, N. H. (1996). In CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3, Ibragimov, N. H., ed., CRC Press, Boca Raton, Florida, Chapter 1, pp. 3–29.

    Google Scholar 

  • Euler, N., Leach, P. G. L., Mahomed, F. M., and Steeb, W.-H. (1988). Int. J. Theor. Phys. 27, 717.

    Google Scholar 

  • Ibragimov, N. H. (1985). Transformation Groups Applied to Mathematical Physics, Reidel, Dordrecht, The Netherlands.

    Google Scholar 

  • Ibragimov, N. H., Kara, A. H., and Mahomed, F. M. (1998). Nonlinear Dynamics 15(2), 115.

    Google Scholar 

  • Kara, A. H., and Mahomed, F. M. (1999). In Proceedings of Modern Group Analysis VII, Ibragimov, N. H., Naqvi, Razi K., and Straume, E., eds., MARS Publishers, Norway, p. 175.

    Google Scholar 

  • Kara, A. H., Vawda, F., and Mahomed, F. M. (1994). Lie Groups Applications 1(2), 27.

    Google Scholar 

  • Kara, A. H., and Mahomed, F. M., and Ñnal, G. (1999). Int. J. Theor. Phys., 38(9), 2389.

    Google Scholar 

  • Laplace, P. S. (1798). Traité de Mécanique Céleste, Vol. 1, Paris [English transl., Celestial Mechanics, New York (1966)].

  • Leach, P. G. L. (1981). J. Austral. Math. Soc. B, 23, 173.

    Google Scholar 

  • Noether, E. (1918). Nachr. König. Gesell. Wiss. Gött. Math.-Phys. Kl. 2, 235 [English transl., Transport Theory Stat. Phys. 1, 186–207 (1971)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Centre for DifferentialEquations, Continuum Mechanics andApplications, University of the Witwatersrand, Wits, 2050, Johannesburg, South Africa

    A. H. Kara

  2. Department of Computational & Applied Mathematics and Centrefor Differential Equations,Continuum Mechanics and Applications, University of the Witwatersrand, Wits, 2050, Johannesburg, South Africa

    F. M. Mahomed

Authors
  1. A. H. Kara
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. M. Mahomed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. M. Mahomed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kara, A.H., Mahomed, F.M. Relationship between Symmetries andConservation Laws. International Journal of Theoretical Physics 39, 23–40 (2000). https://doi.org/10.1023/A:1003686831523

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003686831523

Search

Navigation