Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In the case of the nonlinear Schr\"odinger equation with designed group velocity dispersion, variable nonlinearity, and gain or loss, we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasisolitons and soliton bound states relevant for fiber communication are also exhibited.