Optical solitons, bifurcation, and chaos in the nonlinear conformable Schrödinger equation with group velocity dispersion coefficients and second-order spatiotemporal terms.

In this study, we utilize the new direct mapping method to derive optical soliton solutions for the nonlinear conformable Schrödinger equation, which accounts for group velocity dispersion coefficients and second-order spatiotemporal terms. Leveraging bifurcation and chaos theories, we conduct an in-depth analysis of the planar dynamical system associated with the equation, providing detailed graphical representations of chaotic solutions for the perturbed system. The time series of the planar system, along with a sensitivity analysis of the perturbed system, is visualized through various graphical illustrations to underscore the model's significance and its dynamic behavior in practical applications. We derive a new family of soliton solutions including bell-shaped, dark-bright, and mixed dark-bright solitons which have not been previously reported in the literature. Further, the influence of the conformable derivative parameter and temporal dynamics on these soliton solutions is systematically investigated, highlighting the system's importance in real-world contexts. The results highlight the potential of the proposed model in advancing optical fiber communication technologies, especially for the efficient transmission and control of ultra-fast pulses. This work contributes both theoretical novelty and practical insights into nonlinear wave propagation in advanced photonic systems.