IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i1p55-63.html
   My bibliography  Save this article

The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations

Author

Listed:
  • Wazwaz, Abdul-Majid

Abstract

The tanh method is applied to the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Solitons and periodic solutions for these equations are formally derived. The Painlevé property v=e±u will be employed to back up our analysis and to emphasize the effectiveness of the presented method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:55-63
    DOI: 10.1016/j.chaos.2004.09.122
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790400654X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.09.122?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. Wazwaz, A.M., 2002. "General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 519-531.
    2. Wazwaz, A.M., 2001. "A study of nonlinear dispersive equations with solitary-wave solutions having compact support," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(3), pages 269-276.
    3. 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.
    4. Wazwaz, Abdul-Majid & Taha, Thiab, 2003. "Compact and noncompact structures in a class of nonlinearly dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 171-189.
    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. Jhangeer, Adil & Hussain, Amjad & Junaid-U-Rehman, M. & Baleanu, Dumitru & Riaz, Muhammad Bilal, 2021. "Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    4. Patra, A. & Baliarsingh, P. & Dutta, H., 2022. "Solution to fractional evolution equation using Mohand transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 557-570.
    5. Borhanifar, A. & Kabir, M.M. & Maryam Vahdat, L., 2009. "New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1646-1654.
    6. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    7. 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.
    8. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Chen, Yong & Li, Biao & Zhang, Hongqing, 2004. "New exact solutions for modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 549-559.
    6. Wazwaz, Abdul-Majid & Taha, Thiab, 2003. "Compact and noncompact structures in a class of nonlinearly dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 171-189.
    7. 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.
    8. Wazwaz, A.M., 2002. "General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 519-531.
    9. Xu, Chuanhai & Tian, Lixin, 2009. "The bifurcation and peakon for K(2,2) equation with osmosis dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 893-901.
    10. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
    11. Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
    12. 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.
    13. 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.
    14. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    15. Wazwaz, Abdul-Majid, 2006. "Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 127-135.
    16. Yin, Jun & Lai, Shaoyong & Qing, Yin, 2009. "Exact solutions to a nonlinear dispersive model with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1249-1254.
    17. Sucu, Nuray & Ekici, Mehmet & Biswas, Anjan, 2021. "Stationary optical solitons with nonlinear chromatic dispersion and generalized temporal evolution by extended trial function approach," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. 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.

    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:25:y:2005:i:1:p:55-63. 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.