IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i2p454-462.html
   My bibliography  Save this article

Two reliable methods for solving variants of the KdV equation with compact and noncompact structures

Author

Listed:
  • Wazwaz, Abdul-Majid

Abstract

In this work we use the sine–cosine and the tanh methods for solving variants of the KdV equation. Compact and noncompact physical solutions for these variants with dispersive effects are formally derived. The study also examines the role of coefficients of the derivatives of the equation and its exponents in affecting the physical structures of the solutions.

Suggested Citation

  • Wazwaz, Abdul-Majid, 2006. "Two reliable methods for solving variants of the KdV equation with compact and noncompact structures," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 454-462.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:454-462
    DOI: 10.1016/j.chaos.2005.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905005692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.06.004?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. Zhang, Zhengdi & Bi, Qinsheng, 2005. "Bifurcations of traveling wave solutions in a compound KdV-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1185-1194.
    2. Wazwaz, Abdul-Majid, 2003. "An analytic study of compactons structures in a class of nonlinear dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(1), pages 35-44.
    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. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    2. Kavitha, L. & Prabhu, A. & Gopi, D., 2009. "New exact shape changing solitary solutions of a generalized Hirota equation with nonlinear inhomogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2322-2329.
    3. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    4. Yusufoğlu, E. & Bekir, A. & Alp, M., 2008. "Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine–Cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1193-1197.
    5. Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
    6. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    7. 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.
    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.
    9. Lv, Xiumei & Lai, Shaoyong & Wu, YongHong, 2009. "An auxiliary equation technique and exact solutions for a nonlinear Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 82-90.

    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. Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
    2. Bi, Qinsheng, 2007. "Peaked singular wave solutions associated with singular curves," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 417-423.
    3. Wazwaz, Abdul-Majid, 2005. "The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 55-63.
    4. Tang, Yaning & Xu, Wei & Gao, Liang & Shen, Jianwei, 2007. "An algebraic method with computerized symbolic computation for the one-dimensional generalized BBM equation of any order," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1846-1852.
    5. Wazwaz, Abdul-Majid, 2006. "Compactons and solitary patterns solutions to fifth-order KdV-like equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 273-279.
    6. Wazwaz, Abdul-Majid & Helal, M.A., 2005. "Nonlinear variants of the BBM equation with compact and noncompact physical structures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 767-776.
    7. Wazwaz, Abdul-Majid, 2008. "Analytic study on the one and two spatial dimensional potential KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 175-181.
    8. Wazwaz, Abdul-Majid, 2005. "Generalized forms of the phi-four equation with compactons, solitons and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 580-588.
    9. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.

    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:28:y:2006:i:2:p:454-462. 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.