IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v180y2024ics0960077924000699.html
   My bibliography  Save this article

Existence of localized modes in a frustrated ferromagnetic spin chain with added biquadratic interaction

Author

Listed:
  • Suganya, S.
  • Srividya, B.
  • Prabhu, A.

Abstract

The analytical study on the 1D frustrated ferromagnetic spin chain with added biquadratic exchange interaction by means of quasi-discrete multiple scale approximation is addressed in this report. It is found that the dynamics of the frustrated spin system is governed by the nonlinear Schrödinger (NLS) equation which admits bright and dark localized modes. We analyze the play roles of biquadratic exchange interaction and frustration parameter on the appearance of the bright and dark solitonic profile. The inclusion of the biquadratic interaction significantly increases the number of unstable/stable domain in the whole Brillouin zone. The linear dispersion curves also shift drastically and the value of the critical point of the frustration parameter changes accordingly. We invoke the extended rational sinh–cosh function method to find the exact soliton solution aided with symbolic computation. The set of soliton solution obtained produces the dark type soliton which depends on the strength of the biquadratic exchange interaction. We further employ an elegant algebraic Hirota bilinearization method to construct multisoliton solution. More interestingly, we explore the elastic collision of two bright solitons in the frustrated spin system which can be exploited for high density data transfer in quantum computing. The impact of biquadratic exchange interaction is found to be crucial in frustrated compounds with edge sharing copper oxides and it strongly favors for stability.

Suggested Citation

  • Suganya, S. & Srividya, B. & Prabhu, A., 2024. "Existence of localized modes in a frustrated ferromagnetic spin chain with added biquadratic interaction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
  • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000699
    DOI: 10.1016/j.chaos.2024.114518
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924000699
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.114518?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. Yao Long & Yinghui He & Shaolin Li, 2014. "Multiple Soliton Solutions for a New Generalization of the Associated Camassa-Holm Equation by Exp-Function Method," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, July.
    2. Ma, Yu-Lan & Li, Bang-Qing, 2022. "Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Li, Bang-Qing & Ma, Yu-Lan, 2020. "Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. J. Vahedi & S. Mahdavifar, 2012. "1D frustrated ferromagnetic model with added Dzyaloshinskii-Moriya interaction," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(5), pages 1-8, May.
    5. Kavitha, L. & Prabhu, A. & Gopi, D., 2009. "New exact shape changing solitary solutions of a generalized Hirota equation with nonlinear inhomogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2322-2329.
    6. Kavitha, L. & Srividya, B. & Dhamayanthi, S. & Kumar, V. Senthil & Gopi, D., 2015. "Collision and propagation of electromagnetic solitons in an antiferromagnetic spin ladder medium," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 643-668.
    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. Ma, Yu-Lan & Li, Bang-Qing, 2024. "Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 489-502.
    2. Ustinov, N.V., 2024. "New type of rogue waves," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
    4. Zdravković, Slobodan & Kavitha, Louis & Satarić, Miljko V. & Zeković, Slobodan & Petrović, Jovana, 2012. "Modified extended tanh-function method and nonlinear dynamics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1378-1386.
    5. Cui, Xiao-Qi & Wen, Xiao-Yong & Li, Zai-Dong, 2024. "Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Mahmoud A. E. Abdelrahman & Emad K. El-Shewy & Y. Omar & N. F. Abdo, 2023. "Modulations of Collapsing Stochastic Modified NLSE Structures," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    7. Lou, Yu & Zhang, Yi & Ye, Rusuo & Li, Miao, 2021. "Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    8. Qi, Linming & Liu, Lu & Zhao, Weiliang, 2024. "Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Amira F. Daghistani & Ahmed M. T. Abd El-Bar & Ahmed M. Gemeay & Mahmoud A. E. Abdelrahman & Samia Z. Hassan, 2023. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    10. Acharya, S.P. & Janaki, M.S., 2022. "Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    11. Zhang, Xi & Wang, Yu-Feng & Yang, Sheng-Xiong, 2024. "Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    12. 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).
    13. Liu, Yaqing & Peng, Linyu, 2023. "Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

    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:180:y:2024:i:c:s0960077924000699. 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.