Skip to main content
SpringerLink
Log in
Book cover

Differential Equations - Geometry, Symmetries and Integrability pp 173–185Cite as

Focal Systems for Pfaffian Systems with Characteristics

  • Chapter
  • First Online:

  • 1290 Accesses

Part of the book series: Abel Symposia ((ABEL,volume 5))

Abstract

Focal systems are a generalization to the case of Pfaffian system with characteristics of the classical notion of focal curves for first-order scalar partial diffeerntial equations. We show how focal systems can be used to prove local normal form results for second-order scalar hyperbolic equations in the plane. We also illustrate their use in integration methods for first-order equations.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Bryant, S.S. Chern, R. Gardner, H. Goldschmidt and P. Griffiths, Exterior differential systems, MSRI Publications, 18, Springer, New York, 1991.

    MATH  Google Scholar 

  2. R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II. Partial differential equations, Wiley Classics Library, Wiley, New York, 1989.

    Google Scholar 

  3. R.B. Gardner, A differential geometric generalization of characteristics, Comm. Pure Appl. Math. 22 (1969), 597–626.

    Article  MATH  MathSciNet  Google Scholar 

  4. R.B. Gardner and N. Kamran, Characteristics and the geometry of hyperbolic equations in the plane, J. Differential Equations 104 (1993), no. 1, 60–116.

    Article  MATH  MathSciNet  Google Scholar 

  5. R.B. Gardner and N. Kamran, Normal forms and focal systems for determined systems of two first-order partial differential equations in the plane, Indiana Univ. Math. J. 44 (1995), no. 4, 1127–1162.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Juras, Some classification results for hyperbolic equations F(x, y, u, ux, uy, uxx, uxy, uyy) = 0, J. Differential Equations 164 (2000), no. 2, 296–320.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Burnside Hall, McGill University, Montreal, QC, Canada

    Niky Kamran

Authors
  1. Niky Kamran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Niky Kamran .

Editor information

Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of Tromsoe, Tromsoe, 9037, Norway

    Boris Kruglikov

  2. Dept. Mathematics & Statistics, University of Tromsoe, Tromsoe, 9037, Norway

    Valentin Lychagin

  3. of Science and Technology, Norwegian University, Trondheim, 7034, Norway

    Eldar Straume

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kamran, N. (2009). Focal Systems for Pfaffian Systems with Characteristics. In: Kruglikov, B., Lychagin, V., Straume, E. (eds) Differential Equations - Geometry, Symmetries and Integrability. Abel Symposia, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00873-3_8

Download citation

Publish with us

Policies and ethics

Search

Navigation