It has been known for some time that the solution profile of dispersive equations posed on periodic domains depends heavily on the algebraic properties of time, a phenomenon called Talbot effect in the literature. In particular, the solution can be a continuous fractal curve at irrational times and a simple step function at rational times. In this project we will set up numerical experiments to study this behavior for model nonlinear equations such as the nonlinear Schrodinger and Korteweg-de Vries equations. We are especially interested in quantifying this behavior by numerical evaluation of the box dimension of the solution curves.
Coding experience, preferably with Python, is a must.