IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v171y2023ics0960077923003247.html
   My bibliography  Save this article

An invariance analysis of the Vakhnenko–Parkes Equation

Author

Listed:
  • Hussain, Akhtar
  • Kara, A.H.
  • Zaman, F.D.

Abstract

Lie symmetry analysis of differential equations is an effective technique to compute exact solutions of a differential equation, to reduce number of independent variables or to reduce the order and nonlinearity of the equation. The present article focuses on the symmetry analysis of Vakhnenko–Parkes Equation (VP Equation). At first, Lie point symmetries of the VP Equation that permit an optimal system of one-dimensional subalgebras are discussed and then using the commutator table we construct the discrete symmetries of the VP Equation using the modified Hydon’s method. Also, we compute the exact solutions using symmetry transformations.

Suggested Citation

  • Hussain, Akhtar & Kara, A.H. & Zaman, F.D., 2023. "An invariance analysis of the Vakhnenko–Parkes Equation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003247
    DOI: 10.1016/j.chaos.2023.113423
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923003247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113423?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. Hongwei Yang & Yunlong Shi & Baoshu Yin & Huanhe Dong, 2012. "Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-15, September.
    2. 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.
    3. V. O. Vakhnenko & E. J. Parkes, 2016. "Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-39, February.
    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. Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.
    2. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Vakhnenko, V.O. & Parkes, E.J., 2012. "The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 846-852.

    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:171:y:2023:i:c:s0960077923003247. 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.