2 problems

Let $u(t,x)$ solve the KdV equation … Assume that the initial data $u(0,x)$ is almost periodic in $x$. Deift's conjecture. The solution $u(t,x)$ is almost periodic in time $t$ and…

Let $U(t)$ denote the Koopman operator associated with the KdV flow on the underlying probability space, acting on observables by composition with the flow, and let the projection…