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In this paper we study dispersive wave equation using the method of multiplescales (MMS) and perform several numerical tests to investigate its accuracy.The key feature of our MMS solution is the linearity of the amplitude equationand the complex nature of the time-frequency. The MMS is tested as an initialvalue problem using three choices of the dispersion model, one toy and twoLorentz models. Depending on the parameters of the problem, the amplitudeequation can be both well- or ill-posed. Despite the ill-posedness, the MMSsolution remains a valid approximation of the solution to the originalnonlinear model.

On the numerical accuracy of the method of multiple scales for nonlinear dispersive wave equations