Talbot effect for dispersive partial differential equations

Faculty Member

Burak Erdogan and Nikolaos Tzirakis

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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


Project Difficulty


Undergrad Prerequisites

Coding experience, preferably with Python, is a must.