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Analysis of Lie Symmetries and Dynamic Solitonic Configurations of Various Invariant Solutions for a Heisenberg Ferromagnetic Spin Chain Model in Magnetism Theory

  • Amit Kumar [1] ; Dharmendra Kumar [1] ; Ashwani Saharan [2]
    1. [1] University of Delhi

      University of Delhi

      India

    2. [2] Indian Institute of Technology Kanpur
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This paper primarily examines various analytic solutions to the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. The proposed model holds significant importance in contemporary magnetism theory, where it helps to describe ferromagnetic ordering in nonlinear dynamics. Additionally, it illustrates the magnetic properties of numerous insulating crystals and the interaction of spins. Ferromagnetism is crucial in modern physics and quantum technologies, especially in the development of electronic and faster storage devices like generators, electric motors, and electromagnets. By utilizing the symmetry isomorphism, we derive symmetric generators, Lie point algebra, commutation and adjoint relations between vector fields. Lie symmetry analysis is an essential mathematical approach for deriving closed-form periodic solutions to nonlinear strong coupled PDEs. We broke down the primary issue into its real and imaginary parts, analyzed each separately, and converted them into different nonlinear ordinary differential equations (ODEs). Through numerical computation, we resolved these ODEs and obtained a spectrum of analytic solutions, including trigonometric, JacobiSN, hyperbolic, exponential, and DawsonF forms, which involved arbitrary independent functions and other constant parameters. These innovative solutions have not been documented in the models under study. In this study, the newly discovered solutions encompass singular, dark, bright, breather, and lump-type solitons that have not been previously observed. By chosen suitable freely parameter values, shown that the amplitude of the derived solutions can be modified.

      Graphical depictions of the reported solutions are provided in two and three dimensions along with their contour projections. The applied methodology is effective in obtaining precise soliton solutions for various fractional partial differential equations in complex media. Our research is original and contrasts with previous studies.Mathematica software is employed to verify the accuracy of the computational techniques by substituting them back into the original model.

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