Soliton Solutions in (2+1)-dimensional Ferromagnetic Spin Chain Using New Extended Auxiliary Method

The focus of this paper is to examine the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation with bilinear and anisotropic interaction, which governs the nonlinear dynamics of magnetic systems. HFSC is a generalization of nonlinear Schrödinger (NLS) equation. By using new extended auxiliary method, we successfully derive soliton solutions for the NLS equation that describe the nonlinear spin dynamics of (2+1)-dimensional HFSC equation. The obtained solutions are in the form of hyperbolic and trigonometric functions. Visual representations of the solutions are depicted in three-dimensional as well as two-dimensional forms. We successfully identified antikink, singular, and dark soliton profiles in our solutions. Our analysis focuses on understanding the influence of the uniaxial crystal field anisotropy parameter on the soliton wave. Notably, our findings reveal that variations in the uniaxial crystal field anisotropy significantly impact the amplitude of the soliton wave. To the best of our knowledge, the solutions obtained using our approach are novel and have not been reported in any previous literature.