Abstract
We give explicit formulas for the propagation of a pulse in a dispersive medium governed by a general dispersion relation. In particular, we consider the mean and standard deviation of a propagating pulse and relate them to the parameters of the initial pulse and the dispersion relation. If the dispersion relation is expanded in a Taylor series, higher-order dispersion is when there are terms that are higher than quadratic. We show the effects of the higher-order dispersion on the propagation of the pulse's mean, standard deviation, and contraction/expansion time. Explicit examples will be given.
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