IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010481.html
   My bibliography  Save this article

On the modified Gardner type equation and its time fractional form

Author

Listed:
  • Wang, Gangwei
  • Wazwaz, Abdul-Majid

Abstract

Differential equations play an important role in many scientific fields. In this work, we study modified Gardner-type equation and its time fractional form. We first derive these two equations from Fermi-Pasta-Ulam (FPU) model, and found that these two equations are related with nonlinear Schro¨dinger equation (NLS) type of equations. Subsequently, symmetries and conservation laws are investigated. Finally, Ba¨cklund transformation of conservation laws also presented. In this article, we not only derive these two equations, but also use perturbation analysis to find the connection between them and the Schro¨dinger equation. Another key point is that Ba¨cklund transformation of conservation laws are also obtained. From these results, it is obvious that the Lie group method is a very effective method for dealing with partial differential equations.

Suggested Citation

  • Wang, Gangwei & Wazwaz, Abdul-Majid, 2022. "On the modified Gardner type equation and its time fractional form," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010481
    DOI: 10.1016/j.chaos.2021.111694
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010481
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111694?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. Mancas, Stefan C. & Adams, Ronald, 2019. "Dissipative periodic and chaotic patterns to the KdV–Burgers and Gardner equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 385-393.
    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. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.

    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.

      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:155:y:2022:i:c:s0960077921010481. 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.