Reducible KAM tori for higher dimensional wave equations under nonlocal and forced perturbation

Abstract

In this paper, we prove an infinite dimensional Kolmogorov-Arnold-Moser theorem. As an application, it is shown that there are many small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equations with a real Fourier multiplier, which are under nonlocal and forced perturbations with a special structure in space and short range property.