Invariant tori of full dimension for a nonlinear Schrödinger equation with an almost periodic potential

Abstract

In this paper, we study a nonlinear Schrödinger equation with an almost-periodic potential, subject to periodic boundary conditions. Under appropriate assumptions on the potential, we obtain many small-amplitude, time-almost-periodic solutions for the equation. We improve the Kolmogorov–Arnold–Moser iteration to reduce the almost-periodic potential, especially depending on the space variables. The analysis of the nonlinear perturbation is also the key argument.