Skip to main content
SpringerLink
Log in

An algebro-geometric interpretation of the Bäcklund-transformation for the Korteweg-de Vries equation

  • Published:
Commentarii Mathematici Helvetici

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

  1. Adler, M. andMoser, J.,On a class of polynomials connected with the Korteweg-De Vries equation. Comm. Math. Physics61 (1978) 1–30.

    Article  MathSciNet  Google Scholar 

  2. Airault, H., McKean, H. andMoser, J.,Rational and elliptic solutions of the Korteweg-De Vries equation and a related many body problem. Comm. Pure Appl. Math.30 (1977) 95–148.

    MathSciNet  Google Scholar 

  3. Burchnall, J. andChaundy, T.,Commutative ordinary differential operators. Proc. Roy. Soc. London, Ser. A,118 (1928) 557–583.

    Google Scholar 

  4. Darboux, G.,Leçons sur la théorie générale des surfaces II. Gauthier-Villars, Paris 1889.

    MATH  Google Scholar 

  5. Deift, P.,Applications of a Commutation formula. Duke Math. Journ.45, (1978) 267–310.

    Article  MathSciNet  Google Scholar 

  6. Drach, J.,Sur l'intégration par quadrature de l'équation d 2 y/dx 2=[ϕ(x)+h]·y. C. R. Acad. Sci. Paris168, (1919) 337–340.

    Google Scholar 

  7. Flaschka, H. andMcLaughlin, D.,Some comments on Bäcklund transformations, canonical transformations, and the inverse scattering method. In: Bäcklund Transformations, pp. 253–295. Lecture Notes in Mathematics 515, Springer, Berlin, Heidelberg, New York 1976.

    Chapter  Google Scholar 

  8. Goursat, E.,Le Problème de Bäcklund. Gauthiers-Villars, Paris 1925.

    MATH  Google Scholar 

  9. Ince, E.,Ordinary Differential Equations. Dover, New York 1956.

    Google Scholar 

  10. McKean, H.,Integrable systems and algebraic curves. In: Global Analysis, pp. 83–200. Lecture Notes in Mathematics 755, Springer, Berlin, Heidelberg, New York 1979.

    Chapter  Google Scholar 

  11. McKean, H.,Theta functions, solitons, and singular curves. In: Partial Differential Equations and Geometry, pp. 237–254. Lecture Notes in Pure and Applied Mathematics 48, Marcel Dekker, New York, Basel 1979.

    Google Scholar 

  12. Krichever, I. M.,Methods of algebraic geometry in the theory of non-linear equations. Russ. Math. Surveys32 (1977) 185–213.

    Article  Google Scholar 

  13. Miura, R.,Korteweg-De Vries equation and generalizations I. A remarkable explicit nonlinear transformation. Journ. Math. Phys.9 (1969) 1202–1204.

    Article  MathSciNet  Google Scholar 

  14. Mumford, D.,An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-De Vries equation and related non-linear equations. Proc. Intern. Symp. Algebraic Geometry Kyoto 1977, 115–153.

  15. Serre, J. P.,Groupes algébriques et corps de classes. Herrmann, Paris 1959.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität, Wegelerstr. 10, D 5300, Bonn 1, W.-Germany

    Fritz Ehlers & Horst Knörrer

  2. Mathematisch Instituut Rijksuniversiteit Leiden, Wassenaarseweg 80, 2300 RA, Leiden, The Netherlands

    Fritz Ehlers & Horst Knörrer

Authors
  1. Fritz Ehlers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Horst Knörrer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ehlers, F., Knörrer, H. An algebro-geometric interpretation of the Bäcklund-transformation for the Korteweg-de Vries equation. Commentarii Mathematici Helvetici 57, 1–10 (1982). https://doi.org/10.1007/BF02565842

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02565842

Keywords

Search

Navigation