Colloquium: Milivoje Lukic (Rice University), KdV equation with almost periodic initial data.
Speaker: Milivoje Lukic, Rice University.
Title: KdV equation with almost periodic initial data
Abstract: The KdV equation is known to be integrable for several
classes of initial data, such as decaying, periodic, and finite-gap
quasiperiodic. In this talk, we will describe recent progress for
almost periodic initial data, centered around a conjecture of Percy
Deift that the solution is almost periodic in time. We will discuss
the proof of existence, uniqueness, and almost periodicity in time, in
the regime of absolutely continuous and sufficiently "thick" spectrum.
In particular, this result proves Deift's conjecture for small
analytic quasiperiodic initial data with Diophantine frequency. The
talk is based on joint work with Ilia Binder, David Damanik, and