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Modelling pulse propagation in complex index materials using the method of multiple scales

In this paper we study pulse propagation in complex refractive index materials, modelled by a dispersive wave equation, using the method of multiple scales (MMS), and perform several numerical tests to investigate its accuracy. We assume a complex valued refracting index in a noncentrosymmetric medium with a Kerr response. The key feature of our MMS solution is the linearity of the amplitude equation and the complex nature of the mode-frequency. The MMS is tested as an initial value problem using three different dispersion models. Depending on the parameters of the problem, the amplitude equation can be both well- or ill-posed. Despite the ill-posedness, the MMS solution remains a valid approximation of the solution to the original nonlinear model.