IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4209275.html
   My bibliography  Save this article

The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms

Author

Listed:
  • Wei-Guo Zhang
  • Xing-Qian Ling
  • Xiang Li
  • Shao-Wei Li

Abstract

In this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthermore, on the basis of the two bell-shaped solitary wave solutions of the equation, the explicit expressions of the orbital stability discriminants are deduced to give the orbitally stable and instable intervals for the two solitary waves as the wave velocity changing. Moreover, the influence caused by the interaction between two nonlinear terms is also discussed. From the conclusion, it can be seen that the influences caused by this interaction are apparently when , which shows the complexity of this system with two nonlinear terms. Finally, by deriving the orbital stability discriminant in the form of Gaussian hypergeometric function, the numerical simulations of several main conclusions are given in this paper.

Suggested Citation

  • Wei-Guo Zhang & Xing-Qian Ling & Xiang Li & Shao-Wei Li, 2019. "The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms," Complexity, Hindawi, vol. 2019, pages 1-17, June.
    • Handle: RePEc:hin:complx:4209275
    DOI: 10.1155/2019/4209275
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4209275.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4209275.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4209275?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
    ---><---

    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:hin:complx:4209275. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.