In fiber optic communication systems, the main linear phenomenon that causes optical pulse broadening is called dispersion, which limits the transmission data rate and distance. The principal nonlinear effect, called self-phase modulation, can also limit the system performance by causing spectral broadening. Hence, to achieve optimal system performance, high data rate and low bandwidth occupancy, those effects must be overcome or compensated. In a nonlinear dispersive fiber, properties of a transmitting pulse: width, chirp, and spectra, are changed along the way and are complicated to predict. Although there is a wellknown differential equation, called the Nonlinear Schrodinger Equation, which describes the complex envelope of the optical pulse subject to the nonlinear and dispersion effects, the equation cannot generally be solved in closed form. Although, the split-step Fourier method can be used to numerically determine pulse properties from this nonlinear equation, numerical results are time consuming to obtain and provide limited insight into functional relationships and how to design input pulses. In this dissertation, various analytical models to characterize fiber nonlinearities have been applied, and the ranges of validity of the models are determined by comparing with numerical results. First, the finite difference method is used to solve the Nonlinear Schrodinger Equation; and its range of validity is determined by comparing to the symmetrical split-step Fourier method. Secondly, root-mean-square (RMS) widths are modeled time domain modeled. It is shown that there exists an optimal input pulse width to minimize output pulse width9 based on the derived RMS models, and the functional form of the minimum output pulse width is derived. The analysis and optimization of signal propagation in optical fiber systems are implemented using MATLAB.