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In this paper, the soliton solutions of (2+1)-dimensional Heisenberg ferromagnetic spin-chain model arising in quantum information are obtained using G′/(bG′+G′+a)-Expansion Method. The solutions of the model are plotted in 2d and 3D graphs to show the dynamics of the solutions with effect of the model parameters. Bifurcations and chaotic behavior are analyzed, providing insights into the system’s dynamics. Our results offer a valuable mathematical tool for studying nonlinear wave phenomena, including the discovery of new wave shapes, bifurcations, and chaotic dynamics. The novel application of the G′/(bG′+G+a)-Expansion Method uncovers previously unreported solutions, while the study of bifurcations and chaos enhances our understanding of the model’s applicability.