Ilia Binder: Integrability of the KdV equation with almost periodic initial data.

Abstract: In 2008, P. Deift conjectured that the solution of KdV equation with almost periodic initial data is almost periodic in time. I will discuss the proof of this conjecture (as well as the uniqueness) in the case of the so-called Sodin-Yuditskii type initial data, i.e. the initial data for which the associated Schroedinger operator has purely absolutely continuous spectrum which satisfies certain thickness conditions. In particular, this proves the existence, uniqueness, and almost periodicity of the solutions with small analytic quasiperiodic initial data with Diophantine frequency vector.

This is a joint work with D. Damanik (Rice), M. Goldstein (Toronto) and M. Lukic (Rice).