Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

This research investigates spin dynamic solitonic solutions in the (2+1)-dimensional Heisenberg ferromagnetic spin chains model. The unified and simple equation schemes are used to integrate the model. Through the techniques, various properties of wave nature, such as Dark bell envelope soliton, Bright bell envelope soliton, periodic wave envelope, Kink shape envelope soliton, periodic wave envelope soliton, oscillating wave, harmonically oscillating wave, oscillating wave with increasing and decreasing amplitude waves, sudden increasing of amplitude and sudden decrease to a particular amplitude wave oscillations, are achieved from the solutions. The effects of changing neighboring interaction and uniaxial crystal field anisotropy parameters on the obtained soliton and its amplitudes are explored. The changing values of neighboring interaction parameters are exhibited as an increase in wave height with increasing parametric values, but increasing the values of the uniaxial crystal field anisotropy parameter causes a reduction in wave height. In the mean time, we see that the real part of the same solution exhibits periodic oscillation while the effects of the parameters have the same increasing and decreasing effects. Analysis of modulation stability found due to small change as perturbation solution of the model. We display gain spectrum versus nonlinearity and dispersion effects in 3D plots. All shapes are illustrated in 3D and 2D plots.