Nonlinear wave dynamics and exact solutions of the fractional complex Heisenberg ferromagnetic-type Akbota model: Applications in quantum magnetism

This study explores the nonlinear fractional complex Heisenberg ferromagnet-type Akbota (FCHFA) model, a key mathematical framework for comprehending complex wave phenomena in ferromagnetic materials and other nonlinear systems. Implementing the modified Khater method and Khater III method as potent computational techniques, we unearth novel solutions that illuminate the model’s complex behavior. To guarantee the precision of our outcomes, the Adomian decomposition method is utilized for accuracy evaluation. The FCHFA model holds considerable physical significance as it encapsulates the fundamental dynamics of spin interactions in quantum magnetism, offering a connection between theoretical constructs and practical magnetic systems. Our investigation not only examines the stability criteria and bifurcation attributes of this model but also enriches the comprehensive understanding of nonlinear wave propagation in condensed matter physics. The scholarly influence of this study is substantial, providing fresh perspectives that may improve the design and application of spintronic devices and strengthen the theoretical basis of nonlinear dynamics in ferromagnetic systems. By revealing distinctive wave behaviors and stability traits, our work lays the groundwork for future advancements in both basic research and technological applications.