Chaos-induced soliton dynamics and energy localization under Doppler-broadened in Electromagnetically Induced Transparency media

This study investigates the nonlinear dynamics and structural stability of self-localized optical modes propagating through a Doppler-broadened Electromagnetically Induced Transparency (EIT) atomic medium. Utilizing a mathematical framework derived from the Rodrigue form of Legendre polynomials, we model the evolution of optical pulses S(|Ω1,2|) and their intensities I(|Ω1,2|) as functions of normalized Rabi frequencies, |Ω1|/γ and |Ω2|/γ. Our results reveal a sophisticated phase-to-amplitude mapping where, despite aggressive phase oscillations between bright and dark soliton patterns near the resonance point |Ω1|=0, the system maintains robust structural order. We demonstrate that the interaction between Doppler broadening and EIT creates an energy-trapping mechanism, forcing the pulse into parallel, high-intensity bright soliton ridges separated by a central valley of suppressed intensity. By precisely tuning the pump and coupling parameters |Ω1,2| and phase variables ϕ1,ϕ2 also generated via the Rodrigue form the maximum localized intensity can be scaled from 0.001 to 0.8 (0.1% to 80%). This transition represents a regime of extreme energy compression driven by the Soliton Area Theorem, where the pulse remains shielded from the smearing effects of Doppler broadening. The high degree of coherence and tunability exhibited by these soliton channels suggests transformative applications Neural signal propagation (biophysics models), DNA dynamics and energy transport, Laser surgery and medical ablation, Biosensing using nonlinear optical solitons, Fiber optic sensors (temperature, pressure, strain), Drug delivery systems (nonlinear wave transport), etc.