IDEAS home Printed from https://ideas.repec.org/a/hin/jnlamp/9272347.html
   My bibliography  Save this article

A Potential Constraints Method of Finding Nonclassical Symmetry of PDEs Based on Wu’s Method

Author

Listed:
  • Tonglaga Bai
  • Temuer Chaolu

Abstract

Solving nonclassical symmetry of partial differential equations (PDEs) is a challenging problem in applications of symmetry method. In this paper, an alternative method is proposed for computing the nonclassical symmetry of PDEs. The method consists of the following three steps: firstly, a relationship between the classical and nonclassical symmetries of PDEs is established; then based on the link, we give three principles to obtain additional equations (constraints) to extend the system of the determining equations of the nonclassical symmetry. The extended system is more easily solved than the original one; thirdly, we use Wu’s method to solve the extended system. Consequently, the nonclassical symmetries are determined. Due to the fact that some constraints may produce trivial results, we name the candidate constraints as “potential” ones. The method gives a new way to determine a nonclassical symmetry. Several illustrative examples are given to show the efficiency of the presented method.

Suggested Citation

  • Tonglaga Bai & Temuer Chaolu, 2019. "A Potential Constraints Method of Finding Nonclassical Symmetry of PDEs Based on Wu’s Method," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-14, July.
    • Handle: RePEc:hin:jnlamp:9272347
    DOI: 10.1155/2019/9272347
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AMP/2019/9272347.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AMP/2019/9272347.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/9272347?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chaolu Temuer & Laga Tong & George Bluman, 2020. "Some Connections between Classical and Nonclassical Symmetries of a Partial Differential Equation and Their Applications," Mathematics, MDPI, vol. 8(4), pages 1-16, April.

    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:hin:jnlamp:9272347. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.