IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i1p252-258.html
   My bibliography  Save this article

Traveling wave solutions for nonlinear differential equations: A unified ansätze approach

Author

Listed:
  • Khuri, S.A.

Abstract

The aim of the paper is to introduce a general transformation for constructing analytic solutions for nonlinear differential equations. The main thrust of this alternate approach is to manipulate a unified ansätze to obtain exact solutions that are general solutions of simpler integrable equations. The ansätze is based on either the choice of an integrable differential operator or on a basis set of functions. Trigonometric, hyperbolic, Weierstrass and Jacobi elliptic functions can be used as building blocks for obtaining the exact solutions. The technique is implemented to acquire traveling wave solutions for the KDV–Burgers–Kuramoto equation.

Suggested Citation

  • Khuri, S.A., 2007. "Traveling wave solutions for nonlinear differential equations: A unified ansätze approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 252-258.
  • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:252-258
    DOI: 10.1016/j.chaos.2005.10.106
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905010714
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.10.106?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.

    References listed on IDEAS

    as
    1. Khuri, S.A., 2005. "Soliton and periodic solutions for higher order wave equations of KdV type (I)," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 25-32.
    2. Khuri, S.A., 2005. "New ansätz for obtaining wave solutions of the generalized Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 705-710.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Zhang, Huiqun, 2009. "New exact travelling wave solutions of nonlinear evolution equation using a sub-equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 873-881.
    2. Petropoulou, Eugenia N. & Siafarikas, Panayiotis D. & Stabolas, Ioannis D., 2009. "Analytic bounded travelling wave solutions of some nonlinear equations II," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 803-810.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khuri, S.A., 2008. "Exact solutions for a class of nonlinear evolution equations: A unified ansätze approach," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1181-1188.
    2. Abdul-Majid Wazwaz & Ma’mon Abu Hammad & Ali O. Al-Ghamdi & Mansoor H. Alshehri & Samir A. El-Tantawy, 2023. "New (3+1)-Dimensional Kadomtsev–Petviashvili–Sawada– Kotera–Ramani Equation: Multiple-Soliton and Lump Solutions," Mathematics, MDPI, vol. 11(15), pages 1-11, August.

    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:eee:chsofr:v:32:y:2007:i:1:p:252-258. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.