Beatrice Pelloni

The phenomenon of dispersive revivals

I will give an introduction to the phenomenon of “dispersive quantisation” or “revivals”. Although first reported in 1835 by Talbot, this phenomenon was only studied in the ’90’s, in particular for the periodic free space Schroedinger equation by Berry and al . It was then rediscovered for the Airy equation by Peter Olver in 2010. Since then, a sizeable literature has examined revivals for the periodic problem for linear dispersive equations with polynomial dispersion relation. What I will discuss in this talk is further occurrences of this phenomenon for different boundary conditions, a novel form of revivals for more general dispersion relations and nonlocal equations such as the linearised Benjamin-Ono equation, and nonlinear (integrable) generalisations. This work is joint with Lyonell Boulton, George Farmakis, Peter Olver and David Smith.