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Nonlinear generation modes in easy-axis anisotropy ferromagnetic spin chains with nearest-neighbor coupling

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Abstract

In this paper, we consider the Heisenberg ferromagnetic lattices with single-ion easy-axis anisotropy to show the effects of the nearest-neighbor coupling on discrete modulation instability and localized energy in the forbidden gap. We use the multi-scale scheme to establish the nonlinear Schrödinnger equation from where it was carried out the static breather equation together with the threshold amplitude. Thus, one end of the spin chains was submitted to an external periodic boundary. It results that the nearest-neighbor coupling parameter induced instability in the forbidden frequency gap by increasing the amplitude of the plane wave. The most important feature of this investigation is the fact that the driven amplitude is considered below the threshold amplitude and the nonlinear supratransmission phenomenon arises. These outcome shed light on the fact that the Heisenberg ferromagnetic spin chains with a single-ion easy-axis anisotropy could be used to generate both long-lived temporal localized solitons and nonlinear supratransmission phenomenon.

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Abbreviations

NNC:

Nearest-neighbor coupling

GV:

Group velocity

MI:

Modulation instability

NS:

Numerical simulation

FG:

Forbidden gap

DA:

Driven amplitude

TA:

Threshold amplitude

DF:

Driven frequency

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Authors and Affiliations

  1. Department of Marine Engineering, Limbé Nautical Arts and Fisheries Institute, P.O Box 485, Limbé, Cameroon

    Alphonse Houwe

  2. Department of Basic Science, National Advanced School of Mines and Petroleum Industries, The University of Maroua, P.O Box 08, Kaélé, Cameroon

    Souleymanou Abbagari

  3. Department of Physics, Faculty of Science, The University of Maroua, P.O Box 814,, Maroua, Cameroon

    Youssoufa Saliou

  4. Department of Mathematics, Lafayette College, Easton, PA, USA

    Lanre Akinyemi

  5. Department of Physics, Faculty of Science, The University of Ngaoundèré, P.O Box 454,, Ngaoundèré, Cameroon

    Doka Serge Yamigno

Authors
  1. Alphonse Houwe
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  2. Souleymanou Abbagari
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  3. Youssoufa Saliou
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  4. Lanre Akinyemi
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  5. Doka Serge Yamigno
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Contributions

Souleymanou Abbagari was involved in conceptualization, formal analysis, investigation, methodology, writing the original draft, resources and software. Alphonse Houwe was responsible for conceptualization, investigation, methodology, writing the original draft, resources and software. Youssoufa Saliou contributed to reviewing and editing, and formal analysis. Lanre Akinyemi took part in writing, reviewing and editing, validation, methodology, resources and software. Serge Y. Doka participated in writing, reviewing and editing, formal analysis, resources and supervision.

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Correspondence to Alphonse Houwe or Souleymanou Abbagari.

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Houwe, A., Abbagari, S., Saliou, Y. et al. Nonlinear generation modes in easy-axis anisotropy ferromagnetic spin chains with nearest-neighbor coupling. Eur. Phys. J. Plus 138, 133 (2023). https://doi.org/10.1140/epjp/s13360-023-03754-3

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  • DOI: https://doi.org/10.1140/epjp/s13360-023-03754-3

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