<p>In this paper, the generalized projective Riccati equation method is applied to study the dual-mode nonlinear Schrödinger equation with a generalized power-law nonlinearity and construct various novel soliton solutions. A diverse set of novel optical soliton solutions has been successfully obtained, encompassing wave structures, dark solitons, bright solitons, mixed dark-bright solitons, and kink-type solitons. To illustrate their dynamic behavior and structural characteristics, these solutions are presented through contour plots, along with detailed 2D and 3D graphical simulations. Further, the influence of the conformable derivative parameter and temporal parameter on the optical solitons is analyzed, emphasizing their crucial roles in shaping soliton properties. To deepen our understanding of the planar dynamical system derived from the current model, we employed bifurcation and chaos theories. Furthermore, we explored the chaotic behavior, including the Lyapunov exponent, of the perturbed system and illustrated the resulting solutions through graphical representations. The constructed soliton solutions are directly applicable to modeling pulse propagation in optical fibers, especially in systems governed by dual-mode interactions and nonlinear effects. These solutions help understand how optical signals behave under the influence of nonlinearity, dispersion, and conformable fractional effects, which are crucial in designing efficient, high-speed communication systems.</p>