Skip to main content
SpringerLink
Log in

Bäcklund transformations

  • Invited Papers
  • Conference paper
  • First Online:
Geometrical Approaches to Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 810))

  • 392 Accesses

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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.

References for section 1

  1. Bäcklund A.,V., Math. Ann. 17,285 (1880)

    Article  MathSciNet  Google Scholar 

  2. Bäcklund A.,V., Math. Ann. 19,387 (1883)

    Article  Google Scholar 

  3. Lamb, G.L. article in "Bäcklund Transformations" (ed. R.M. Miura, Springer Verlag,Berlin-Heidelberg-New York) S.L.N.maths.515, 1976

    Google Scholar 

  4. Skyrme, T.H.R., Proc. Roy. Soc. 262A,237(1961)

    Article  MathSciNet  Google Scholar 

  5. Rogers, C. S.L.N.maths. 515,106(1976)

    Google Scholar 

  6. Loewner,C. NASA Tech. Note 2 1/4 65(1950)

    Google Scholar 

  7. Forsyth,A.R. "Theory of Differential Equations", 5&6, Dover Publications (1959).

    Google Scholar 

  8. Lie, S. "Sophus Lies's 1880 Transformation Group paper" eds. N. Wallach & R. Hermann Math.Sci.Press Brookline (1976).

    Google Scholar 

  9. Backlund A.V., Math.Ann., 13, 69. (1877)

    Article  Google Scholar 

  10. Gardener R.B., Trans.Amer.Math.Soc., 126, 514. (1967)

    Article  MathSciNet  Google Scholar 

  11. Ibragimov N, Anderson R.L., J.Math.Anal&Appl., 59, 145. (1977)

    Article  MathSciNet  Google Scholar 

  12. Gardener R.B., "Constructing Backlund Transformations" Invited address at the Berlin conference on Differential Geoemtry and Global Analysis July 1977.

    Google Scholar 

  13. Clairin,Ann.Sci de l'Ecole Normal Superieure, 19(3), supplement (1902)

    Google Scholar 

  14. Liouville J. de Math.Pures et Appl.Paris, 18 (1), 72. (1853)

    Google Scholar 

  15. Eisenhart L.P., "A treatise on the differential geometry of curves and surfaces" Dover N.Y.

    Google Scholar 

  16. Goursat E., Memor.Sci.Math. 6, Gautier Villars, Paris 1925.

    Google Scholar 

  17. Cartan E., Les systemes Differentielles Exterieures at Leurs Applications Geometrique, Hermann, Paris, 1946.

    Google Scholar 

  18. Hermann R., "The geometry of non-linear differential equations, Backlund transformations and solitons" 12A&B. Math. Sci.Press Brookline Massachusettes 1976.

    MATH  Google Scholar 

  19. Scott A, Chu F.Y, McLaughlin D.W., IEEE, 1443, Oct 1973.

    Google Scholar 

  20. Wahlquist H, Estabrook F., J.Math.Phys. 16, 1 (1975) and 17, 1993 (1976)

    Article  MathSciNet  Google Scholar 

  21. Pirani F, Robinson D.C, Shadwick W, Local Jet Bundle formulation of Backlund Transformations,Reidel 1979.

    Google Scholar 

References for section 2

  1. Thirring W, Ann.Phys., 3, 91. (1958)

    Article  MathSciNet  Google Scholar 

  2. Wahlquist H, Estabrook F., J.Math.Phys., 16, 1. (1975)

    Article  MathSciNet  Google Scholar 

  3. Wahlquist H, Estabrook F., J.Math.Phys., 17, 1993. (1976)

    MathSciNet  Google Scholar 

  4. Wahlquist H, Estabrook F, Hermann R., "Differential Geometric Prolongations and Backlund Transformations" in the Proc. Ames Sem. on Differential and Algebraic Geometry for Control Engineers (Brookline: Math.Sci.Press 1977)

    Google Scholar 

  5. Dodd R, Gibbon J., Proc.R.Soc.Lond.A. 359, 411. (1978)

    Article  MathSciNet  Google Scholar 

  6. Holod P., "Pseudopotentials and Backlund Transformations for the Thirring equation" Institute for theoretical physics(Kiev)preprint 78–100.(1978)

    Google Scholar 

  7. Morris H., J.Phys.A., 12, 131. (1979)

    Article  Google Scholar 

  8. Morris H., J.Math.Phys., 19, 85 (1978)

    Article  Google Scholar 

  9. Pohlmeyer K., Comm.Math.Phys., 46, 207. (1976)

    Article  MathSciNet  Google Scholar 

  10. Luscher M, Pohlmeyer K., Nuclear Physics B137, 46. (1978)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  12. Harrison K., Phys.Rev.Lett 41, 1197. (1978)

    Article  MathSciNet  Google Scholar 

  13. Harrison K., "A large family of vacuum solutions of the equations of general relativity" submitted to Phys.Rev.Lett. June 1979.

    Google Scholar 

  14. Maison D., Phys.Rev.Lett., 41, 521. (1978)

    Article  MathSciNet  Google Scholar 

  15. Maison D., J.Math.Phys., 20, 871. (1979)

    Article  MathSciNet  Google Scholar 

  16. Morris H, Dodd R., "A 2-connection and operator bundles for the Ernst equation for axially symmetric gravitational fields" Physics Letters (to appear)

    Google Scholar 

  17. Morris H., "Inverse scattering problems in higher dimensions: Yang-Mills fields and the supersymmetric sine-Gordon equation" J.Math.Phys. (to appear)

    Google Scholar 

  18. Fornberg B, Whitam G., Phil. Trans.R.Soc.Lond., 289, 373. (1978)

    Article  Google Scholar 

  19. Benjamin T., J.Fluid Mech., 29, 559. (1967)

    Article  Google Scholar 

  20. Ono H., J.Phys.Soc.Japan, 39, 1082. (1975)

    Article  MathSciNet  Google Scholar 

  21. Joseph R., J.Phys. A10, L225. (1977)

    Google Scholar 

  22. Satsuma J,Ablowitz M, Kodama Y., "On an internal wave equation describing a stratified fluid with finite depth" Physics Letters (to appear)

    Google Scholar 

  23. Bock T, Kruskal M., Physics Letters, 74A, 173. (1979)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trinity College, Dublin 2, Ireland

    R. K. Dodd & H. C. Morris

Authors
  1. R. K. Dodd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. C. Morris
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rodolfo Martini

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Dodd, R.K., Morris, H.C. (1980). Bäcklund transformations. In: Martini, R. (eds) Geometrical Approaches to Differential Equations. Lecture Notes in Mathematics, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089974

Download citation

  • DOI: https://doi.org/10.1007/BFb0089974

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10018-8

  • Online ISBN: 978-3-540-38166-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation