Talbot effect for dispersive partial differential equations

Faculty Member

Burak Erdogan and Nikolaos Tzirakis

Project Image

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.

Team Meetings

Bi

Project Difficulty

Intermediate

Undergrad Prerequisites

Coding experience, preferably with Python, is a must.