The Department of Applied Mathematics is pleased to host this series of colloquium lectures, funded in part by a generous gift from the Boeing Company. This series will bring to campus prominent applied mathematicians from around the world.
Title: Non-smooth behaviour of linearised water waves: the Talbot effect revisited
Abstract: I will describe some surprising phenomena that appear when periodic linearised wave models such as the linear KdV, BO, or ILW equations are considered with a discontinuous initial condition. These phenomena are analogous to the “Talbot effect” observed in the 1850’s in linear optics.
I will show the result of experiments as well as the mathematical analysis of the models, and discuss the dependence of this effect on the linearity and the boundary conditions, to conclude that it is remarkably robust, leaving its echo in the solution of a wide variety of problems.
Youtube: Watch the talk online here.