Skip to main content
Log in

Exterior Differential Systems with Symmetry

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry group of a differential equation to find noninvariant solutions.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, I. M. and Fels, M. E. Hyperbolic Exterior Differential Systems with Symmetry, in preparation.

  • Anderson, I. M., Fels, M. E. and Torre, C. G. (2000) Group invariant solutions without transversality, Comm. Math. Phys. 212(3), 653–686.

    Article  Google Scholar 

  • Anderson, I. M., Kamran, N. and Olver, P. J. (1992) Internal, external and generalized symmetries, Adv. Math. 100(1), 53–100.

    Article  Google Scholar 

  • Bluman, G. and Anco, S. (2002) Symmetry and Integration Methods for Differential Equations, Springer-Verlag.

  • Bluman, G. and Kumei, S. (1989) Symmetries and Differential Equations, Appl. Math. Sci. 81, Springer-Verlag.

  • Bryant, R. L. (1995) An Introduction to Lie Groups and Symplectic Geometry. Geometry and Quantum Field Theory, Amer. Math. Soc.

  • Bryant, R. L., Chern, S. S., Gardner, R. B., Goldschmidt, H. L. and Griffiths, P. A. (1991) Exterior Differential Systems, Spinger-Verlag.

  • Bryant, R. L. and Griffiths, P. A. (1995) Characteristic cohomology of differential systems. II. Conservation laws for a class of parabolic equations, Duke Math. J. 78, 531–676.

    Article  Google Scholar 

  • Bryant, R. L., Griffiths, P. A. and Hsu, L. (1995) Hyperbolic exterior differential systems and their conservation laws, Part I, Selecta Math., N.S. 1, 21–112.

    Google Scholar 

  • Fels, M. E. (2004) Integrating scalar ordinary differential equations with symmetry revisited, in preparation.

  • Itskov, V. (2001) Orbit reduction of contact ideals, Contemp. Math. 285, 171–181.

    Google Scholar 

  • Krasilcshchik, I. S. and Vinogradov, A. M. (1984) Nonlocal symmetries and the theory of coverings Local symmetries and conservation laws, Acta Appl. Math. 2, 21–78.

    Article  Google Scholar 

  • Kumpera, A. (1999) On the Lie and Cartan theory of invariant differential systems, J. Math. Sci. Univ. Tokyo. 6, 229–314.

    Google Scholar 

  • Olver, P. J. (1998) Applications of Lie Groups to Differential Equations, Springer-Verlag.

  • Osvianikov, L. V. (1982) Group Analysis of Differential Equations, Academic Press.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. M. Anderson.

Additional information

Mathematics Subject Classifications (2000)

58A15, 34A26.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, I.M., Fels, M.E. Exterior Differential Systems with Symmetry. Acta Appl Math 87, 3–31 (2005). https://doi.org/10.1007/s10440-005-1136-y

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-005-1136-y

Keywords

Navigation