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We investigate the evolution of an optical pulse in a dispersive, nonlinear dielectric material. The technique exploits two adiabatic invariants, action and wave number. The analysis is performed in detail for a nonlinear variant of the Lorentz model. We find that there are two nonlinear generalizations of the linear group velocity. From this we predict that optical shocks can form on either the front or back edge of the wave form.

Light Pulse Propagation in Nonlinear Dispersive Medium