IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i5p2257-2264.html
   My bibliography  Save this article

Analytic approximations for the one-loop soliton solution of the Vakhnenko equation

Author

Listed:
  • El-Nahhas, A.

Abstract

In this paper, we give an analytic solution for the one-loop soliton solution of the Vakhnenko equation, by the use of the homotopy analysis method and via a fractional basis.

Suggested Citation

  • El-Nahhas, A., 2009. "Analytic approximations for the one-loop soliton solution of the Vakhnenko equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2257-2264.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2257-2264
    DOI: 10.1016/j.chaos.2007.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907008892
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.10.013?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. Huang, Ding-jiang & Li, De-sheng & Zhang, Hong-qing, 2007. "Explicit N-fold Darboux transformation and multi-soliton solutions for the (1+1)-dimensional higher-order Broer–Kaup system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1677-1685.
    2. Al-Mdallal, Qasem M. & Syam, Muhammad I., 2007. "Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1610-1617.
    3. Wu, Yongyan & Wang, Chun & Liao, Shi-Jun, 2005. "Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1733-1740.
    4. Wu, Xiao-Fei & Ge, Hong-Liang & Ma, Zheng-Yi, 2007. "Exact discrete soliton solutions of the nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 940-946.
    5. Xu, Gui-qiong & Li, Zhi-bin, 2005. "On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1363-1375.
    6. Dai, Zhengde & Li, Shaolin & Dai, Qingyun & Huang, Jian, 2007. "Singular periodic soliton solutions and resonance for the Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1148-1153.
    Full references (including those not matched with items on IDEAS)

    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. Dai, Zhengde & Huang, Ying & Sun, Xing & Li, Donglong & Hu, Zhenhua, 2009. "Exact singular and non-singular solitary-wave solutions for Kadomtsev–Petviashvili equation with p-power of nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 946-951.
    2. Belmonte-Beitia, Juan & Pérez-García, Víctor M. & Vekslerchik, Vadym, 2007. "Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1268-1277.
    3. Sajid, M. & Hayat, T., 2008. "The application of homotopy analysis method to thin film flows of a third order fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 506-515.
    4. Aydın, Ayhan, 2009. "Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 735-751.
    5. Zeng, Xiping & Dai, Zhengde & Li, Donglong, 2009. "New periodic soliton solutions for the (3+1)-dimensional potential-YTSF equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 657-661.
    6. Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.
    7. Liu, Yinping & Li, Zhibin, 2009. "The homotopy analysis method for approximating the solution of the modified Korteweg-de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 1-8.
    8. Alomari, A.K. & Noorani, M.S.M. & Nazar, R., 2009. "On the homotopy analysis method for the exact solutions of Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1873-1879.
    9. Mohammed K. Elboree, 2014. "Applications of the extended test approach to (2 + 1)-dimensional Gardner equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(4), pages 433-441, August.
    10. Sajid, M. & Hayat, T., 2009. "The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1317-1323.
    11. 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.
    12. Ye, Caier & Zhang, Weiguo, 2011. "New explicit solutions for (2+1)-dimensional soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1063-1069.
    13. He, Dongdong & Pan, Kejia, 2015. "A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 323-336.

    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:40:y:2009:i:5:p:2257-2264. 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.