David Damanik (Rice)

Almost Periodicity in Time of Solutions of the KdV Equation

We describe joint work with Ilia Binder, Michael Goldstein and Milivoje Lukic, which is motivated by the following conjecture of Percy Deift: Solutions of the KdV equation with almost periodic initial data are almost periodic in time. Our work confirms this conjecture in so-called Sodin-Yuditskii regime, that is, assuming that the Schrodinger operator whose potential is given by the initial datum has purely absolutely continuous spectrum (along with some mild assumptions on the topological structure of the spectrum).