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Arising wave propagation in nonlinear media for the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model

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  • Seadawy, Aly R.
  • Nasreen, Naila
  • Lu, Dianchen
  • Arshad, Muhammad

Abstract

In this study, we study the (2+1)-dimensional nonlinear Schrödinger kind equation which illustrates the non-linear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains (HFSCs) through bilinear and anisotropic interactions in the semi-classical limit. This model also illustrates the ferromagnetic materials of magnetic ordering. Two analytical schemes are employed to study the equation namely, improved auxiliary equation and generalized Riccati mapping methods. We construct dark and bright solitons, combined bright–dark solitons, periodic waves, solitary waves and elliptic solutions to this equation. We give graphical presentations of the 2D and 3D of some achieved solutions. The obtained results of this investigation might be useful to explain the physical structure of this model. The achieved results of HFSC show the effectiveness and reliability of the proposed techniques.

Suggested Citation

  • Seadawy, Aly R. & Nasreen, Naila & Lu, Dianchen & Arshad, Muhammad, 2020. "Arising wave propagation in nonlinear media for the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s037843711931619x
    DOI: 10.1016/j.physa.2019.122846
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    References listed on IDEAS

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    1. Seadawy, Aly R., 2016. "Stability analysis solutions for nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a magnetized electron–positron plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 44-51.
    2. Seadawy, Aly R., 2015. "Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 124-131.
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    1. Bakıcıerler, Gizel & Alfaqeih, Suliman & Mısırlı, Emine, 2021. "Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Seadawy, Aly R. & Arshad, Muhammad & Lu, Dianchen, 2020. "The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Thongchai Botmart & M. El-Morshedy, 2022. "Wiener Process Effects on the Solutions of the Fractional (2 + 1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation," Mathematics, MDPI, vol. 10(12), pages 1-9, June.

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