In this study, we explore the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation because of its significant role in modeling the nonlinear spin-wave propagation and magnetic excitations in ferromagnetic materials. The aim is to develop exact analytical solutions of the model through two different methods: a modified (addendum-type) Kudryashov method and a unified Riccati equation method. These methods provide a range of exact wave solutions, such as periodic, hyperbolic, trigonometric and rational structures, which exhibit a rich nonlinear behavior of the model. The solutions are discussed and depicted graphically in 2D and 3D forms, exhibiting stable, bounded, and finite propagation of waves without singularities. A key novelty of this study lies in the combined application of the two analytical methods to the HFSC model, which has not been extensively explored in previous literature. The outcome indicates the success and compatibility of these methods in describing the nonlinear behavior of spin-wave structures. The results could be applied for the study of nonlinear magnetic structures and may find applications in spintronics and modeling of ferromagnetic materials.
Jawarneh et al. (Wed,) studied this question.