IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p908-d366966.html
   My bibliography  Save this article

Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation

Author

Listed:
  • Asıf Yokus

    (Department of Actuary, Faculty of Science, Firat University, Elazig 23200, Turkey
    These authors contributed equally to this work.)

  • Hülya Durur

    (Department of Computer Engineering, Faculty of Engineering, Ardahan University, Ardahan 75000, Turkey
    These authors contributed equally to this work.)

  • Hijaz Ahmad

    (Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan)

  • Shao-Wen Yao

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)

Abstract

In this paper, a new solution process of ( 1 / G ′ ) -expansion and ( G ′ / G , 1 / G ) -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical ( G ′ / G , 1 / G ) -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave solutions, whereas traveling wave has an important place in applied sciences and illuminates many physical phenomena. 3D, 2D and contour graphs are displayed to show the stationary wave or the state of the wave at any moment with the values given to these constants. Conditions that guarantee the existence of traveling wave solutions are given. Comparison of ( G ′ / G , 1 / G ) -expansion method and ( 1 / G ′ ) -expansion method, which are important instruments in the analytical solution, has been made. In addition, the advantages and disadvantages of these two methods have been discussed. These methods are reliable and efficient methods to obtain analytic solutions of nonlinear evolution equations (NLEEs).

Suggested Citation

  • Asıf Yokus & Hülya Durur & Hijaz Ahmad & Shao-Wen Yao, 2020. "Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:908-:d:366966
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/908/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/908/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ali, Karmina K. & Yilmazer, Resat & Yokus, Asıf & Bulut, Hasan, 2020. "Analytical solutions for the (3＋1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    2. Ahmad, Hijaz & Seadawy, Aly R. & Khan, Tufail A., 2020. "Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 13-23.
    3. Kaya, Doǧan & Yokus, Asif, 2002. "A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(6), pages 507-512.
    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. Elgazery, Nasser S., 2008. "Numerical solution for the Falkner–Skan equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 738-746.
    2. Ali, Karmina K. & Yokus, Asıf & Seadawy, Aly R. & Yilmazer, Resat, 2022. "The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Fardi, Mojtaba & Khan, Yasir, 2021. "A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Momani, Shaher, 2006. "Non-perturbative analytical solutions of the space- and time-fractional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 930-937.
    5. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.

    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:gam:jmathe:v:8:y:2020:i:6:p:908-:d:366966. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.