Nonlinear chirped pulse in a dispersion compensated system

We study nonlinear pulse propagation in an optical transmission system with dispersion compensation. This is particularly important for designing a ultra-fast long-haul communication system in the next generation. There exists a quasi-stationary pulse solution in such a system whose width and chirp are rapidly oscillating with the period of dispersion compensation. This pulse also has several new features such as enhanced power when compared with the soliton case with a uniform dispersion and a deformation from the sech-shape of soliton. We use the averaging method, and the averaged equation to describe the core of the pulse solution is shown to be the nonlinear Schrodinger equation having a nontrapping quadratic potential. Because of this potential, a pulse propagating in such a system eventually decays into dispersive waves in a way similar to the tunneling effect. However in a practical situation, the tunneling effect is estimated to be small, and the decay may be neglected.