Study on the (2+1)-dimensional quantum Heisenberg ferromagnetic spin chain model: envelope optical bright and dark soliton solutions and other traveling wave solutions

This work deals with one of the most fundamental evolutionary equations that arises in quantum mechanics and is widely used in quantum information, as well as in understanding magnetic phenomena and material properties, namely the Heisenberg ferromagnetic spin chain (HFSC) model. Thus, we investigate a nonlinear (2+1)-dimensional Heisenberg model that describes the propagation of nonlinear waves in quantum mechanics and other physical mediums. The model incorporates both linear and nonlinear dispersion, describing the dynamics of magnetic materials. This work presents interesting findings, including bright, dark, periodic, and rational solutions, as well as other traveling wave solutions. We implement a variety of powerful schemes to derive these diverse optical soliton solutions. Moreover, we derive more solutions of distinct structures, which include periodic and exponential solutions. The obtained results enhance the understanding of the dynamics of higher-dimensional nonlinear wave equations, which can be applied to model various nonlinear modulated structures in plasma physics, fluids, and optics.