It is the goal of applied mathematics to study mathematical models of physical systems to elucidate their operation principles. The development of simple theoretical models requires a strong interaction between experimentalists and theoreticians. especially in the case of phenomenological models, where parameter values in a propsed model are fitted, so that the model output is in good agreement with experiments. In general many parameter values entering a derived or proposed model are determined by experiments while the theoretical models are typically used to improve the device design or to determine the optimum operation conditions. The purpose of this thesis is to elucidate some of the physics of interest in the field of semiconductor laser modelling, semiconductor optics and fiber optics. To be more specific we will investigate: The Colliding-Pulse Mode-Locked (CPM) Quantum Well (QW) laser diode; the excitonic semiconductor response for varying material thickness in the case of linear optics; and modulational instability of electromagnetic waves in media with spatially varying non-linearity.