Commuting flows and invariant tori: Korteweg-de Vries (Q1181241)

The author considers the equation \(\partial u/\partial t=K(u)\), where \(K(u)\) is a nonlinear operator and \(u\) is in the class of smooth periodic functions (with period one). Let \(F_ m(u)\) denote smooth functionals that are in involution and constant along solutions of the equation. It is determined in which sense the level sets of the functions \(F_ m\) are an infinite-dimensional torus and the flow of the equation is almost periodic in time. The results are applied to the periodic KdV equation.