∂A/∂t = μA + (D + ic₁)∂²A/∂x² + (β + ic₃)|A|²A
Unlike conservative solitons (KdV), dissipative solitons exist only in driven-dissipative systems. They are fixed-point attractors in function space — shape and velocity determined by parameters, not initial conditions. Gain (μ > 0) is balanced by saturation (β < 0). Found in lasers, chemical oscillators, plasma, and reaction-diffusion systems (Akhmediev & Ankiewicz).