IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i09ns0218348x22501791.html
   My bibliography  Save this article

Fractional Complex Transforms, Reduced Equations And Exact Solutions Of The Fractional Kraenkel–Manna–Merle System

Author

Listed:
  • LIHUA ZHANG

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China)

  • ZHENLI WANG

    (��School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China)

  • BO SHEN

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China)

Abstract

Exact solutions of the fractional Kraenkel–Manna–Merle system in saturated ferromagnetic materials have been studied. Using the fractional complex transforms, the fractional Kraenkel–Manna–Merle system is reduced to ordinary differential equations, (1 + 1)-dimensional partial differential equations and (2 + 1)-dimensional partial differential equations. Based on the obtained ordinary differential equations and taking advantage of the available solutions of Jacobi elliptic equation and Riccati equation, soliton solutions, combined soliton solutions, combined Jacobi elliptic function solutions, triangular periodic solutions and rational function solutions, for the KMM system are obtained. For the obtained (1 + 1)-dimensional partial differential equations, we get the classification of Lie symmetries. Starting from a Lie symmetry, we get a symmetry reduction equation. Solving the symmetry reduction equation by the power series method, power series solutions for the KMM system are obtained. For the obtained (2 + 1)-dimensional partial differential equations, we derive their bilinear form and two-soliton solution. The bilinear form can also be used to study the lump solutions, rogue wave solutions and breathing wave solutions.

Suggested Citation

  • Lihua Zhang & Zhenli Wang & Bo Shen, 2022. "Fractional Complex Transforms, Reduced Equations And Exact Solutions Of The Fractional Kraenkel–Manna–Merle System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-15, December.
  • Handle: RePEc:wsi:fracta:v:30:y:2022:i:09:n:s0218348x22501791
    DOI: 10.1142/S0218348X22501791
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22501791
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0218348X22501791?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.

    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:wsi:fracta:v:30:y:2022:i:09:n:s0218348x22501791. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.