IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-7524-0_29.html
   My bibliography  Save this book chapter

Geometric Deformations of the Evolution Equations and Bäcklund Transformations

In: The Mathematical Legacy of Eduard Čech

Author

Listed:
  • Bohumil Cenkl

    (Northeastern University, Department of Mathematics)

Abstract

The sine-Gordon equation (2ω)xi + sin(2ω) = 0 describes a surface with constant negative curvature. Sasaki [3], demonstrated that pseudospherical surfaces are associated with many evolution equations. The surfaces of negative curvature (not necessarily constant), which can be thought of as deformations of the pseudospherical surfaces, are defined by solutions of a system of equations. We call such a system a deformed sine-Gordon system. The geometry of such systems has been extensively studied in the theory of line congruences [2]. It turns out that the more appropriate setting for the study of the geometry in full generality is not the group of euclidean motions but the projective group. In that case we talk about W-systems. It is clear that such a theory is an important special case of the study of the σ-models. The significant feature of the deformed sine-Gordon and W-systems is’ the existence of Bäcklund transformations and the validity of the permutability theorem.

Suggested Citation

  • Bohumil Cenkl, 1993. "Geometric Deformations of the Evolution Equations and Bäcklund Transformations," Springer Books, in: Miroslav Katětov & Petr Simon (ed.), The Mathematical Legacy of Eduard Čech, pages 436-438, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7524-0_29
    DOI: 10.1007/978-3-0348-7524-0_29
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-0348-7524-0_29. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.