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Impurity–impurity and impurity–breather interactions combined with energy localization in a quantum 1D Klein–Gordon chain

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  • Djoufack, Z.I.
  • Ribama, R. Abouem A.
  • Nguenang, J.P.

Abstract

This paper investigates an analytical and numerical study on impurity–impurity and impurity–breather interactions associated with energy localization in a quantum 1D Klein–Gordon chain. The nonlinear Schrödinger equation (NLSE) is obtained with the use of Glauber’s coherent states in addition to a multiple time scale method. The resonant structures are found via the frequency spectrum around the critical impurity mass. The condition of existence of breather and impure localized mode are acquired. The dynamics of the impurity mode can be significantly controlled by the impurity mass. The accuracy of the analytical approach is validated by an excellent agreement with the finding of numerical simulation. When the breather interacts with two impure modes, several behaviors such as trapping, chaotic trapping, well, excitation in addition to total and partial reflection are found. From the modulational instability (MI) probed, we have found from the direct numerical simulations that long-term evolution of modulated wave exhibits chaotic behavior. Finally, energy localization through MI is conducted and a good agreement between the theoretical analysis and the numerical simulations is observed.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001091
    DOI: 10.1016/j.chaos.2023.113208
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    References listed on IDEAS

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    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. 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.
    3. 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.
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