IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v95y2022i5d10.1140_epjb_s10051-022-00337-6.html
   My bibliography  Save this article

Breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain

Author

Listed:
  • R. Abouem A. Ribama

    (University of Douala)

  • Z. I. Djoufack

    (Fotso Victor University Institute of Technology, University of Dschang
    The African Institute for Mathematical Sciences (AIMS))

  • J. P. Nguenang

    (University of Douala)

Abstract

We study the breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain. By using the second quantification operators, we transform classical Hamiltonian into its quantum version, through Glauber’s coherent state representation in addition to the multiple-scale method, the 2D nonlinear Schrödinger equation (NLSE) is obtained. This NLSE is analytically solved by adopting the Rayleigh–Ritz variational method. Around impurity’s critical mass, we prove the existence of resonant structure. This critical mass is observed when plotting the frequency spectrum under the effect of the impurity mass and harmonic force constants. The effects of impurity mass and the harmonic force constants are found in the amplitude frequency spectra. When the breather interacts with the impurity, the system exhibit different scenario that are: barrier, well, excitation and chaotic all related to the trapping phenomenon. The modulational instability (MI) which helps to confirm the existence of breather is investigated. We have shown that impurity strength increases the instability regions, and the MI growth rate can be dramatically affected by the impurity mass around the critical value. Graphic abstract

Suggested Citation

  • R. Abouem A. Ribama & Z. I. Djoufack & J. P. Nguenang, 2022. "Breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(5), pages 1-19, May.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:5:d:10.1140_epjb_s10051-022-00337-6
    DOI: 10.1140/epjb/s10051-022-00337-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-022-00337-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-022-00337-6?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. Djoufack, Z.I. & Kenmogne, Fabien & Nguenang, J.P. & Kenfack-Jiotsa, A., 2021. "Dynamics of solitons with periodic loops intrinsic localized modes and modulational instability in a quantum 2D nonlinear square Klein-Gordon chain," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. A. Alvarez & F. R. Romero & J. F.R. Archilla & J. Cuevas & P. V. Larsen, 2006. "Breather trapping and breather transmission in a DNA model with an interface," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(1), pages 119-130, May.
    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. Djoufack, Z.I. & Ribama, R. Abouem A. & Nguenang, J.P., 2023. "Impurity–impurity and impurity–breather interactions combined with energy localization in a quantum 1D Klein–Gordon chain," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    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. Djoufack, Z.I. & Ribama, R. Abouem A. & Nguenang, J.P., 2023. "Impurity–impurity and impurity–breather interactions combined with energy localization in a quantum 1D Klein–Gordon chain," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Li, Bang-Qing & Ma, Yu-Lan, 2022. "Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing electromagnetic systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

    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:spr:eurphb:v:95:y:2022:i:5:d:10.1140_epjb_s10051-022-00337-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.