IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/6557949.html
   My bibliography  Save this article

Travelling Wave Solutions of Nonlinear Evolution Problem Arising in Mathematical Physics through (G′/G)-Expansion Scheme

Author

Listed:
  • Siyuan Fan
  • Tianyi Sun
  • Peng Liu
  • Dongmin Yu
  • Wen-Tsao Pan

Abstract

This article deals with the application of well-known (G′/G)-expansion to investigate the travelling wave solutions of nonlinear evolution problems including the Boussinesq equation, Klein–Gordon equation, and sine-Gordon equation as these problems appear frequently in mathematical physics. The beauty of the suggested method is to transform the highly nonlinear evolution equation into a system of nonlinear algebraic equations by means of trial solution and auxiliary equation. It is found that the presented approach is simple, efficient, has a less computational cost, and produced rational trigonometric solutions. In order to investigate the novel results, various simulations have been executed. It is renowned that all solutions are in the form of soliton with a single hump and singular which is travelling as time increases gradually. It travels as time travel with the same shape. Moreover, as A2 decreases the amplitude of the solutions decreases. A comparative study illustrates that some of the obtained solution matches with the existing results against particular values of parameters and various new travelling wave solution attained the first time. The method seems more appropriate by means of a computational work. It can also be extended to demonstrate the behavior of other physical models of physical nature.

Suggested Citation

  • Siyuan Fan & Tianyi Sun & Peng Liu & Dongmin Yu & Wen-Tsao Pan, 2022. "Travelling Wave Solutions of Nonlinear Evolution Problem Arising in Mathematical Physics through (G′/G)-Expansion Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, July.
  • Handle: RePEc:hin:jnlmpe:6557949
    DOI: 10.1155/2022/6557949
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/mpe/2022/6557949.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/mpe/2022/6557949.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2022/6557949?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:jnlmpe:6557949. 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.