IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920305555.html
   My bibliography  Save this article

Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system

Author

Listed:
  • Kumar, Vineesh
  • Patel, Arvind

Abstract

This paper addresses the soliton solutions of the Mel’nikov system by the complex amplitude ansatz method and the He’s variational principle. The bright, anti-bright, dark, anti-dark, kink, anti-kink, bell-shaped, breather and homoclinic orbits are obtained as different possible solutions of the Mel’nikov system by the two methods. The solutions and their dynamical behaviour captured by the two methods are discussed. The solutions contain enough number of free physical parameters. These solutions give a better explanation of the associated physical phenomena. The modulation instability analysis of the steady-state solutions of the Mel’nikov system is investigated. This investigation has revealed that the Mel’nikov system is stable against small perturbation for a certain range of perturbation wave numbers. Apart from this, these solutions also help in validating the amount of accuracy in the numerical solutions and to perform the stability analysis further.

Suggested Citation

  • Kumar, Vineesh & Patel, Arvind, 2020. "Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305555
    DOI: 10.1016/j.chaos.2020.110159
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920305555
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110159?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. Wazwaz, Abdul-Majid, 2005. "Generalized forms of the phi-four equation with compactons, solitons and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 580-588.
    2. Porsezian, K. & Murali, R. & Malomed, Boris A. & Ganapathy, R., 2009. "Modulational instability in linearly coupled complex cubic–quintic Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1907-1913.
    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. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.

    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:140:y:2020:i:c:s0960077920305555. 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.