Dispersive perturbations of solitons of the nonlinear Schrödinger equation

A useful analysis of dispersive (radiative) perturbations of solitons of the nonlinear Schrödinger equation is developed. With reference to the propagation of optical solitons in glass fibers, the analysis is used to treat the collision of a low-intensity wave packet with a soliton, the radiation field created by the local perturbation of a soliton, and finally that created by a spatially periodic perturbation of the parameters of the fiber, or equivalently by a periodic variation in gain and loss that averages to zero. Perturbations whose wavelength is short compared with the soliton period produce exponentially small radiation fields as a result of the need for phase matching.

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