Soliton Propagation

Physics: Optical soliton: SPM (self-phase modulation) balances GVD (group velocity dispersion). NLSE: ∂A/∂z = i(β₂/2)∂²A/∂T² + iγ|A|²A. Fundamental soliton (N=1): P₀ = |β₂|/(γT₀²), sech-shaped pulse. N-th order soliton breathes with period z₀ = πT₀²/(2|β₂|). Hasegawa & Tappert (1973) predicted; Mollenauer (1980) demonstrated in optical fiber. N=0.5→1: pulse narrows to soliton; N=1: shape-preserving; N=2,3: higher-order solitons breathe periodically. Rogue waves are oceanic analogs. Gordon-Haus jitter from ASE limits soliton-based transmission distances.