Modeling Optical Technologies with Continuous and Discrete Nonlinear Schrödinger Equations

This thesis considers continuous and discrete models that describe optical technologies. In the continuous setting, the interaction of modulated pulses in nonlinear dispersive media is addressed. It is shown that there is almost no interaction of two modulating pulse solutions with different carrier waves, regardless of the envelope type. In the discrete setting, the existence, stability, and bifurcation structure of localized solutions are examined in one and two dimensions.