Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations

Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations - Lars Hakan Eliasson

Lars Hakan Eliasson
University of Paris VI; Institute for Advanced Study
February 21, 2012
We shall discuss reducibility of these equations on the torus with a small potential that depends quasi-periodically on time. Reducibility amounts to "reduce” the equation to a time-independent linear equation with pure point spectrum in which case all solutions will be of Floquet type.

For the Schrodinger equation, this has been proven in a joint work with S. Kuksin, and for the wave equation we shall report on a work in progress with B. Grebert and S. Kuksin.