Chaos-induced scalar-to-vector soliton transitions in birefringent chiral media driven by Rodrigues–Legendre fields

This study investigates the spatiotemporal dynamics of self-localized optical modes in a chiral atomic medium under birefringent conditions, where the driving fields are constructed using the Rodrigues representation of Legendre polynomials. We demonstrate a transition from scalar to vector soliton regimes governed by the interplay between linear birefringence and Kerr nonlinearity. Numerical simulations of the soliton field S(z,t) and its corresponding intensity I(z,t) show that nonlinear self-trapping effectively compensates birefringence-induced temporal walk-off, enabling the formation of coherent vector soliton states. The localized intensity of the soliton can be tuned within the range 0.4% to 98%, while the peak amplitude of S(z,t) varies from 0.0025 to 0.56. These solitons preserve their structural integrity over extended propagation distances, maintaining stable peak amplitudes and asymptotically vanishing temporal tails. We further identify distinct dynamical regimes, including stationary vector solitons with negligible relative group velocity and multi-soliton trains exhibiting velocity locking under birefringent perturbations. The persistence of localized intensity without dispersive broadening confirms robust high-contrast confinement. These results provide a framework for controlled manipulation of vector solitons in atomic media, with potential relevance to nonlinear wave dynamics and optical information processing. The modified result applicable in quantum information transport in Bose–Einstein condensates, specialized optical pulse shaping, nonlinear signal modulation, precision rotation sensing, soliton-mediated switching in photo refractive media, advanced wave guiding and quantum simulations.