IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v303y2017icp165-170.html
   My bibliography  Save this article

Symmetries, travelling-wave and self-similar solutions of the Burgers hierarchy

Author

Listed:
  • Sinuvasan, R.
  • Tamizhmani, K.M.
  • Leach, P.G.L.

Abstract

We examine the general element of the Burgers Hierarchy, ut+∂∂x(∂∂x−u)nu=0,n=0,1,2,…, for its Lie point symmetries. We use these symmetries to construct traveling-wave and self-similar solutions. We observe that the general member of the hierarchy can be rendered as a linear (1+1)-evolution equation by means of an elementary Riccati transformation and examine this equation for its Lie point symmetries. With the use of these symmetries we can construct the traveling-wave and self-similar solutions in closed form.

Suggested Citation

  • Sinuvasan, R. & Tamizhmani, K.M. & Leach, P.G.L., 2017. "Symmetries, travelling-wave and self-similar solutions of the Burgers hierarchy," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 165-170.
    • Handle: RePEc:eee:apmaco:v:303:y:2017:i:c:p:165-170
    DOI: 10.1016/j.amc.2017.01.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317300504
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.01.036?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Andrey V. Minakov & Victoria D. Meshkova & Dmitry Viktorovich Guzey & Maksim I. Pryazhnikov, 2023. "Recent Advances in the Study of In Situ Combustion for Enhanced Oil Recovery," Energies, MDPI, vol. 16(11), pages 1-26, May.

    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:eee:apmaco:v:303:y:2017:i:c:p:165-170. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.