Dynamical wave phenomena requires the understanding of the large time behaviour of partial differential equations. Quantum Mechanics is one such example. Optical and laser systems are of similar nature. Such analysis poses a special challenge both to theorists and computational analysis. The study of various aspects of the nonlinear Schrödinger equation by analytic and numerical methods is proposed. The topic and its nature will be determined according to the interests and experience of the student.
Analysis of various Fast Fourier Transforms to determine accuracy, and to hopefully better understand the floating-point error involved. Specifically, implementing the FFTW algorithm in C on trial data sets, and researching IEEE standards.