IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2131-d627708.html
   My bibliography  Save this article

Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation

Author

Listed:
  • Almudena P. Márquez

    (Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain)

  • María S. Bruzón

    (Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain)

Abstract

This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie’s symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning.

Suggested Citation

  • Almudena P. Márquez & María S. Bruzón, 2021. "Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation," Mathematics, MDPI, vol. 9(17), pages 1-11, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2131-:d:627708
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2131/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/17/2131/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:9:y:2021:i:17:p:2131-:d:627708. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.