IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-2110-4_7.html
   My bibliography  Save this book chapter

Potential Symmetries of Partial Differential Equations

In: Symmetry Analysis of Differential Equations with Mathematica®

Author

Listed:
  • Gerd Baumann

    (University of Ulm, Department of Mathematical Physics)

Abstract

The last two chapters discussed point symmetries and non-classical symmetries. These types of symmetry are local symmetries because the coordinates are involved in the local transformations in a direct way. This chapter discusses a completely different type of symmetry. We not only consider the original PDEs A = 0 but also derived systems of PDEs whose solutions are solutions of the original equations. The new associated system of PDEs is treated by the methods discussed in the previous sections. The result of this treatment are symmetries not only depending on the local variables of the original equation but also on variables of the affiliated system of PDEs. Thus, we get a new type of symmetry depending on an extended set of variables. Such symmetries are generally called non-local symmetries. A special type of non-local symmetry is a potential symmetry. Our interest in this chapter are potential symmetries of PDEs.

Suggested Citation

  • Gerd Baumann, 2000. "Potential Symmetries of Partial Differential Equations," Springer Books, in: Symmetry Analysis of Differential Equations with Mathematica®, chapter 7, pages 392-403, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2110-4_7
    DOI: 10.1007/978-1-4612-2110-4_7
    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

    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:978-1-4612-2110-4_7. 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.