Chirped optical solitons

We consider the evolution of nonlinear optical pulses in some inhomogeneous optical media wherein the pulse propagation is governed by the nonlinear Schrödinger equation with variable dispersion. The Painlevé analysis is applied to obtain the condition for the soliton pulse propagation. Two dispersion profiles satisfying this criterion are the constant dispersion and exponentially decreasing dispersion profiles. In the exponentially varying dispersive media, we explain the existence and the formation of chirped optical soliton through the variational equation for the chirp. In addition, we theoretically discuss the generation of exact chirped higher order solitons using the Hirota bilinear method. We also demonstrate the implication for optical communications systems in terms of pulse compression by using these exact chirped solitons. Finally, we analyze the interaction scenarios of the chirped higher order solitons.