IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i1p464-472.html
   My bibliography  Save this article

Solitary wave solutions for the KdV and mKdV equations by differential transform method

Author

Listed:
  • Kangalgil, Figen
  • Ayaz, Fatma

Abstract

In this paper, we aim to present a reliable algorithm in order to obtain exact and approximate solutions for the nonlinear dispersive KdV and mKdV equations with initial profile. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. We first present the definition and operation of the two-dimensional differential transform and investigate the soliton solutions of Kdv and mKdV equations are obtained by the present method. Therefore, in the present work, numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

Suggested Citation

  • Kangalgil, Figen & Ayaz, Fatma, 2009. "Solitary wave solutions for the KdV and mKdV equations by differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 464-472.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:464-472
    DOI: 10.1016/j.chaos.2008.02.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908000581
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.02.009?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. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    2. Zhu, Yonggui & Chang, Qianshun & Wu, Shengchang, 2005. "Exact solitary-wave solutions with compact support for the modified KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 365-369.
    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. Ravi Kanth, A.S.V. & Aruna, K., 2009. "Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2277-2281.
    2. H. M. Abdelhafez, 2016. "Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method," Mathematics, MDPI, vol. 4(1), pages 1-12, March.

    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. Mawia Osman & Yonghui Xia & Omer Abdalrhman Omer & Ahmed Hamoud, 2022. "On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-49, June.
    2. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    3. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    4. Jin-Shun, Feng & Ming-Pu, Guo & Deyou, Yuan, 2009. "The presentation of explicit analytical solutions of a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2422-2428.
    5. Zhu, Yonggui & Tong, Kang & Chaolu, Temuer, 2007. "New exact solitary-wave solutions for the K(2,2,1) and K(3,3,1) equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1411-1416.
    6. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.
    7. Lan, Heng-you & Cui, Yi-Shun, 2009. "A neural network method for solving a system of linear variational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1245-1252.
    8. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.

    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:41:y:2009:i:1:p:464-472. 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.