Skip to main content
SpringerLink
Log in

On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations

  • Chapter
Algebraic Aspects of Integrable Systems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 26))

Abstract

Invariance under Laplace-Darboux-type transformations is established for the 2+1-dimensional Loewner-Konopelchenko-Rogers integrable system. This is exploited to derive a chain of novel, integrable Ernst-type equations which contain an arbitrary parameter.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P.S. Laplace, Recherches sur le Calcul Intégral aux Différences Partielles, Mémoires de l’Academie Royale des Sciences de Paris (1773).

    Google Scholar 

  2. G. Darboux, Leçons sur la Théorie Générale des Surfaces, Gauthier- Villars, Paris (1887).

    MATH  Google Scholar 

  3. L.P. Eisenhart, Transformation of Surfaces, Chelsea, New York (1962).

    Google Scholar 

  4. E.P. Lane, Projective Differential Geometry of Curves and Surfaces, The University of Chicago Press, Chicago (1932).

    Google Scholar 

  5. M. Toda, J. Phys. Soc. Japan 22 (1967), 431.

    Article  Google Scholar 

  6. B.G. Konopelchenko, Phys. Lett. A 156 (1991), 221.

    Article  MathSciNet  Google Scholar 

  7. M. Boiti, J.J.P. Leon and F. Pempinelli, Inverse Problems 3 (1987), 25.

    Article  MathSciNet  MATH  Google Scholar 

  8. B.G. Konopelchenko and C. Rogers, Phys. Lett. A 158 (1991), 391.

    Article  MathSciNet  Google Scholar 

  9. B.G. Konopelchenko and C. Rogers, J. Math. Phys. 34 (1993), 214.

    Article  MathSciNet  MATH  Google Scholar 

  10. W.K. Schief, Proc. R. Soc. London A 446 (1994), 381.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Oevel and C. Rogers, Rev. Math. Phys. 5 (1993), 299.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Oevel and W. Schief, Rev. Math. Phys. 6 (1994), 1301.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Ernst, Phys. Rev. 167 (1968), 1175.

    Article  Google Scholar 

  14. F. Ernst, Phys. Rev. 168 (1968), 1415.

    Article  Google Scholar 

  15. A.S. Fokas and M.J. Ablowitz, J. Math. Phys. 23 (1982), 2033.

    Article  MathSciNet  MATH  Google Scholar 

  16. W.K. Schief, J. Phys. A: Math. Gen. 27 (1994), 547.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, The University of New South Wales, Sydney, 2052, Australia

    W. K. Schief & C. Rogers

Authors
  1. W. K. Schief
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Rogers
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College, SW7 2BZ, London, UK

    A. S. Fokas

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    I. M. Gelfand

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Birkhäuser Boston

About this chapter

Cite this chapter

Schief, W.K., Rogers, C. (1997). On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2434-1_16

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7535-0

  • Online ISBN: 978-1-4612-2434-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation