IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v31y2007i1p95-104.html
   My bibliography  Save this article

The extended F-expansion method and its application for a class of nonlinear evolution equations

Author

Listed:
  • Abdou, M.A.

Abstract

By means of a simple transformation technique, we have shown that the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, a new Hamiltonian amplitude equation, generalized Hirota–Satsuma coupled system and generalized ZK-BBM equation can be reduced to the elliptic-like equation. Then, the extended F-expansion method is used to obtain a series of solutions including the single and the combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear evolution equations.

Suggested Citation

  • Abdou, M.A., 2007. "The extended F-expansion method and its application for a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 95-104.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:95-104
    DOI: 10.1016/j.chaos.2005.09.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905008866
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.09.030?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.

    Citations

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


    Cited by:

    1. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    2. Ye, Caier & Zhang, Weiguo, 2011. "New explicit solutions for (2+1)-dimensional soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1063-1069.
    3. Bekir, Ahmet & Boz, Ahmet, 2009. "Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 458-465.
    4. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
    5. Erbaş, Barış & Yusufoğlu, Elçin, 2009. "Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2326-2330.
    6. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    7. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Tariq, Kalim U. & Bekir, Ahmet & Nisar, Sana, 2023. "The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    9. Verma, Pallavi & Kaur, Lakhveer, 2019. "Integrability, bilinearization and analytic study of new form of (3+1)-dimensional B-type Kadomstev–Petviashvili (BKP)- Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 879-886.
    10. Feiyun Pei & Guojiang Wu & Yong Guo, 2023. "Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    11. Han, Tianyong & Li, Zhao & Li, Chenyu, 2023. "Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    12. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    13. Velasco-Juan, M. & Fujioka, J., 2020. "Integral complex modified Korteweg-de Vries (Icm-KdV) equations," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    14. Wafaa B. Rabie & Hamdy M. Ahmed & Walid Hamdy, 2023. "Exploration of New Optical Solitons in Magneto-Optical Waveguide with Coupled System of Nonlinear Biswas–Milovic Equation via Kudryashov’s Law Using Extended F-Expansion Method," Mathematics, MDPI, vol. 11(2), pages 1-28, January.
    15. Mandal, Uttam Kumar & Malik, Sandeep & Kumar, Sachin & Zhang, Yi & Das, Amiya, 2024. "Integrability aspects, rational type solutions and invariant solutions of an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    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:31:y:2007:i:1:p:95-104. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.